Permutation Combination Prof:- Jimmy Sethna 1. In how many ways can 5 rings be worn on the four fingers of your left hand? 2. Mary has 7 roses, 8 lilies and 10 carnations. In how many ways can a bouquet be made if she has to choose 3 roses, 5 lilies and 6 carnations? 3. Three Maths books, four English and four reasoning books are kept on a shelf. In how many ways they can be arranged so that the books of each type are always together? 4. How many three letter words can be constructed using all the 26 letters if only the middle letter of each word has to be a vowel? 5. In how many ways can 5 identical black balls and 7 identical white balls be arranged in a row so that no two black balls are together? 6. In how many ways can all 7 sweets be distributed to three friends Jack , Jill and Tom so that Jill always gets 2 sweets and each of them gets at least one sweet. 7. In how many ways can 4 men and 4 women sit at a round table with no two women in consecutive position 8. A box contains 7 red, 6 white and 4 blue balls. Select of 3 balls so that (i) none is red (ii) one of each color are selected 9. How many numbers greater than thousand can be made using the digits 1, 0, 3, 4 and 5 without repetition 10. A mocktail has to be prepared from three kinds of whiskey, 4 kinds of soda and five kinds of fruit juice. How many mocktails can be made taking at least one of each kind? 11. Barbara has 8 shirts and 9 pants. How many clothing combinations does Barbara have, if she doesn't wear 2 specific shirts with 3 specific pants? 12. A credit card number has 6 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 6, the forth is divisible by 3 and the fifth digit is 3 times the sixth. How many different credit card numbers exist? 13. In how many ways can you sit 8 people on a bench if 3 of them must sit together? 14. In how many ways can you sit 7 people on a bench if Kruti won't sit on the middle seat or on either end? 1 15. In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 green balls. How many balls must be taken out in order to make sure we took out 8 of the same color? 16. In a jar there are 21 white balls, 24 green balls and 32 blue balls. How many balls must be taken out in order to make sure we have 23 balls of the same 17. How many 5 digit numbers can be created if the following terms apply: the leftmost digit is even, the second is odd, the third is a non even prime and the fourth and fifth are two random digits not used before in the number? 18. In how many ways a cricket team of 11 Players can be selected out of 15 Players . If (i) one particular player must be there in each team (ii) One particular player is excluded from each team. 19. In how many ways can seven different pictures be hung in a row so that one specific picture is (i) at the center (ii) at either end 20. In a zoo, there are 5 different cages for 5 tigers. One of them is too small for 2 big tigers. In how many ways can the 5 tigers be arranged? 21. In how many ways can 7 people be arranged at a round table so that two particular persons be always together ? 22. A father takes 8 children, 3 at a time to the Zoo, as often as he can without taking the same three together more than once (i) How often will each child go (ii) how often will he go. 23. In a workshop there are 4 kinds of beds, 3 kinds of closets, 2 kinds of shelves and 7 kinds of chairs. In how many ways can a person decorate his room if he wants to buy one shelf, one bed and one of the following: a chair or a closet? 24. Three Girls are to be seated on a bench. How many different sitting arrangements are possible if Alisha must sit next to Ankita? 2