Find the value of 10C3?
CO3 2. In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women? CO3 3. (Direction 3-5):A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has (i) No girls ? CO3 4. (ii) At least one boy and one girl ? CO3 5. (iii) At least three girls ? CO3 6. A box contains three white balls, four black balls and three red balls. The number of ways in which three balls can be drawn from the box so that at least one of the balls is black is : CO3 7. The number of four–digit telephone numbers having at least one of their digits repeated is : CO3 8. In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together? CO3 9. How many words can be formed by using all letters of the word ‘STUDENT? CO3 10. In how many different ways can the letters of the word EXTRA be arranged so that the vowels are never come together? CO3 11. How many 4-letters words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed? CO3 12. How many 6 digit telephone numbers can be formed if each number starts with 35 and no digit appears more than once? CO3 13. Find the number of ways in which the letters of the word 'MACHINE' can be arranged such that the vowels may occupy only odd positions.? CO3 14. In how many ways can a cricket eleven be chosen out of a batch of 15 players if there is no restriction on the selection? CO3 15. In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected so that at least one boy should be selected? CO3 16. DIRECTION (16-25)-WRITE THE CORRECT CONCLUSION Statement I: Some gold are platinum II: Some platinum are silver III: Some silver are zinc Conclusion I: Some gold are silver II: Some zinc are platinum
CO4
17. Statement I: Only a few rivers are lakes II: All rivers are ocean III: All oceans are stream Conclusion I: All stream being lakes is a possibility II: At least some oceans are rivers CO4 18. Statement I: Only biscuits are chocolate II: Only few biscuits are snacks III: All snacks are beverages Conclusion I: Some biscuits are not snacks is a possibility II: Some chocolates are snacks is a possibility
CO4 19. Statement I: Some mobiles are telephone II: No cordless is mobile. III: Some tablets are mobiles Conclusion I: No mobile is cordless II: All telephone being tablets is a possibility
CO4 20. Statement I: Some Gmail is yahoo II: No yahoo is Instagram III: All Instagram is twitter Conclusion I: Some twitter being Gmail is a possibility II: Some yahoo can never be Instagram
CO4 21. Statements: I.Some pens are keys. Some keys are locks. II.All locks are cards. III.No card is a paper Conclusions: I.No lock is paper. II.Some cards are keys III.Some keys are not paper.
CO4 22. Statements: I.Some papers are books. II.All papers are words. Conclusion s: I.All words being books is a possibility. II.Some words are not papers CO4 23. Statements: I.No animal is a dog. II.Some monkeys are animals. III.All cats are dogs. Conclusions: I.No animal is a monkey. II.All dogs are definitely not animals.
CO4 24. Statements: I.No animal is a dog. II.Some monkeys are animals. III.All cats are dogs. Concluions: I.Some animals are monkeys. II.No cat is an animal.
CO4 25. Statements: I.No day is a week. II.Some months are days. III.No week is a year. Conclusions: I.No day is a year. II.Some months are not week
need answer
nCr = n! / (r!(n-r)!) 10C3 = 10! / (3!(10-3)!) 10C3 = (1098) / (321) 10C3 = 120
Total ways = 7C5 * 3C2 Total ways = (7! / (5! * (7-5)!)) * (3! / (2! * (3-2)!)) Total ways = (21 *3) Total ways = 63
(i) No girls: Selecting 5 boys from 7 can be done in 7C5 ways, which equals 21 ways.
(ii) At least one boy and one girl: This is the complement of the previous case, so it's the total number of ways to select a team (11C5) minus the ways to select a team with no girls, which is 21. Total ways = 11C5 - 21 Total ways = 462 - 21 Total ways = 441 ways
(iii) At least three girls: Selecting 3 girls from 4 can be done in 4C3 ways, which equals 4 ways.
The number of ways to draw three balls such that at least one is black is the total ways to draw 3 balls minus the ways to draw 3 balls with no black balls: Total ways = (10C3) - (6C3) Total ways = (120) - (20) Total ways = 100 ways
The number of four–digit telephone numbers having at least one of their digits repeated can be calculated as follows: Total possible 4-digit numbers = 9 * 10 * 10 * 10 (1 can't be 0) Total numbers with all distinct digits = 9 * 9 * 8 * 7 (1st digit can't be 0) Number with at least one repeated digit = Total possible - Total distinct Number with at least one repeated digit = (9 * 10 * 10 * 10) - (9 * 9 * 8 * 7) Number with at least one repeated digit = 8100 - 4536 Number with at least one repeated digit = 3564 numbers
The number of different ways the letters of the word 'LEADING' can be arranged, with the vowels always together, can be calculated as follows: Consider the group of three vowels (EAI). There are 4 consonants and 3 vowels grouped together. This gives 5! ways to arrange within the group. The number of arrangements within the group is 5!. The number of arrangements for the group itself is 3!. The total number of arrangements = 3! * 5! = 6 * 120 = 720.
The number of words by using all the letters of the word ‘STUDENT’ can be calculated as 7!/(2!). (We divide by 2! because of the repeating letters T and N.) The total number of words = 7! / 2! = 2520.
The number of different ways the letters of the word 'EXTRA' can be arranged, such that the vowels are never together, can be calculated as: ways - (number of ways with vowels together) = 5! - (4! * 2) = 120 - 48 = 72 ways.
The number of 4-letter words that can be formed out of the letters of the word 'LOGARITHMS', without repetition, can be calculated as 10P4 = 1098*7 = 5040.
The number of 6-digit telephone numbers that be formed if each number starts with 35 and no digit appears more than once is 88765*4 = 40,320.
The number of ways in which the letters of the word 'MACHINE' can be arranged such that the vowels occupy only odd positions can be calculated as follows: The word 'MACHINE' has 7 letters. There are 4 consonants and 3 vowels. The odd positions are 1st, 3rd, 5th, and 7th. The number of ways to arrange the 4 consonants in the odd positions = 4P4 = 4! = 24.
The number of ways a cricket eleven can be chosen out