Class XI Chapter 7 – Permutation and Combination Maths ______________________________________________________________________________ Question 8: Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king. Solution 8: From a deck of 52 cards, 5-card combinations have to be made in such a way that in each selection of 5 cards, there is exactly one king. In a deck of 52 cards, there are 4 kings. 1 king can be selected out of 4 kings in 4 C 1 ways. 4 cards out of the remaining 48 cards can be selected in Thus, the required number of 5-card combinations is 48 C 4 C 48 48 1 4 ways. C . Question 9: It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible? Solution 9: 4 men and 4 women are to be seated in a row such that the women occupy the even places. The 5 men can be seated in 5! Ways. For each arrangement, the 4 women can be seated only at the cross marked places (so that women occupy the even places). Therefore, then women can be seated in 4! ways. Thus, possible number of arrangements 4! 5! 24120 2880 Question 10: From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen? Solution 10: From the class of 25 students, 10 are to be chosen for an excursion party. Since there are 3 students who decide that either all of them will join or none fo them will join, there are two cases. Case I: All the three students join. Then, the remaining 7 students can be chosen from the remaining 22 students in 22 C 7 ways. Case II: None of the three students join. Then, 10 students can be chosen from the remaining 22 students in 22 C 10 ways. Thus, required number of ways of choosing the excursion party is C C 22 22 7 10 . 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 ______________________________________________________________________________ Question **11**: In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together? Solution **11**: In the given word ASSASSINATION, the letter A appears 3 times, S appears 4 times, I appears 2 times, N appears 2 times, and all the other letters appear only once. Since all the words have to be arranged in such a way that all the Ss are together, SSSS is treated as a single object for the time being. This single object together with the remaining 9 objects will account for 10 objects. These 10 objects in which there are 3 As, 2 Is, and 2 Ns can be arranged in Thus, Required number of ways of arranging the letters of the given word 10! 3!2!2! ways. 10! 151200 3!2!2! . Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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