Question

1. In how many ways can a casting director choose a female lead and a male lead from five female actors and six male actors?

2. For a segment of a radio show, a disc jockey can play 7 songs. If there are 13 songs to select from, in how many ways can the program for this segment be arranged?

3. Suppose you are asked to list, in order of preference, the three best movies you have seen this year. If you saw 20 movies during the year, in how many ways can the three best be chosen and ranked?

Answer 1

1. 1 female lead can be chosen in 5C1 ways

1 male lead can be chosen in 6C1 ways

   nCr = n ! / r! (n-r)!

No of ways of chosing a female and male lead = 5C1 * 6C1 = 5 * 6 = 30

ANS 30 ways

2. For arraging a segment the order of 7 songs can be changed, hence pemutations

   No of ways the program for this segment be arranged = 13 P 7 = 8,648,640

nPr = n ! / (n-r)!

ANS : 8,648,640

3. 3 best movies from 20 movies in order of preference, hence permutations.

No of many ways can the three best be chosen and ranked = 20P3 = 6840

ANS : 6840