At a benefit concert, seven bands have volunteered to perform but there is only

Question

At a benefit concert, seven bands have volunteered to perform but there is only enough time for four of the bands to play. a. How many different lineups are possible? b. Is this a permutation or combination? Explain. At a benefit concert, seven bands have volunteered to perform but there is only enough time for four of the bands to play. a. How many different lineups are possible? b. Is this a permutation or combination? Explain. a. How many different lineups are possible? b. Is this a permutation or combination? Explain.

Explanation / Answer

Dear Student Thank you for using Chegg a) Total Number of ways of selection of 4 bands from 7 bands is 7C4 = 35 Now since the order is important, the selected 4 bands can lineup in 4! Ways 4! = 24 Hence total number of ordered lineups possible 7C4 * 4! = 840 b) This is a question of permutation. Incase of combination order of selection is not important but whenever order is important one has to use permutation theorm Hence as per part a) reply above solution was 7C4*4! which is equal to 7P4 7P4 = 7!/3! 7C4*4! = (7!/4!3!)*4! = 7!/3! Hence sovled

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