Class XI Chapter 7 – Permutation and Combination Maths ______________________________________________________________________________ 3 boys can be selected from 5 boys in 3 girls can be selected from 4 girls in 5 C 3 4 C 3 ways. ways. Therefore, by multiplication principle, number of ways in which a team of 3 boys and 3 girls 5 4 5! 4! can be selected C3 C3 3!2! 3!1! 5 43! 43! 3! 2 3! 10 4 40 Question 5: Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls each colour. Solution 5: There are a total of 6 red balls, 5 white balls, and 4 blue balls. 9 balls have to be selected in such a way that each selection consists of 3 balls of each colour. Here, 3 balls can be selected from 6 red balls in 6 C 3 ways. 3 balls can be selected from 5 white balls in 5 C 3 ways. 3 balls can be selected from 5 blue balls in 5 C 3 ways. Thus, by multiplication principle, required number of ways of selecting 9 balls. 6 5 5 6! 5! 5! C3 C3 C3 3!3! 3!2! 3!2! 65 43! 5 43! 5 43! 3! 3 2 3! 21 3! 21 201010 2000 Question 6: Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination. Solution 6: In a deck of 52 cards, there are 4 aces. A combinations of 5 cards have to be made in which there is exactly one ace. Then, one ace can be selected in 4 C 3 ways and the remaining 4 cards can be selected out of the Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 7 – Permutation and Combination Maths ______________________________________________________________________________ 48 cards in 48 C 4 ways. Thus, by multiplication principle, required number of 5 card combinations 48 4 48! 4! C4 C1 4!44! 1!3! 48 47 46 45 4! 4! 3 21 778320 Question 7: In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of **11** must include exactly 4 bowlers? Solution 7: Out of 17 players, 5 players are bowlers. A cricket team of **11** players is to be selected in such a way that there are exactly 4 bowlers. 4 bowlers can be selected in 5 C 4 ways and the remaining 7 players can be selected out of the 12 players in 12 C 7 ways. Thus, by multiplication principle, required number of ways of selecting cricket team 5 12 5! 12! 12**11**1098 C4 C7 5! 3960 4!1! 7!5! 5! 43 21 Question 8: A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected. Solution 8: There are 5 black and 6 red balls in the bag. 2 black balls can be selected out of 5 black balls in 5 C 2 ways and 3 red balls can be selected out of 6 red balls in 6 C 3 ways. Thus, by multiplication principle, required number of ways of selecting 2 black and 3 red balls 5 6 5! 6! 5 4 65 4 C2 C3 10 20 200 . 2!3! 3!3! 2 321 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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