Question: A school has 14 teachers out of which 8 are male. A team of 8 teachers is to be formed with 4 female teachers. In how many ways can the team be formed?
A ) 1060 B ) 1050 C ) 1070 D ) 1040
Steps to derive
1 Number of female teachers = 14 - 8 = 6 [Subtract.]
2 Number of ways to select 4 female teachers out of 6 female teachers = 6C4 = 6!(6-4)!×4! = 6!2!×4! = 15
3 Number of ways to select 4 male teachers out of 8 male teachers = 8C4 = 8!(8-4)!×4! = 8!4!×4! = 70
4 Number of ways in which the team can be formed = Number of ways to select 4 female teachers × Number of ways to select 4 male teachers
[Substitute and multiply.] 5 = 15 × 70 = 1050
6 A team of 8 teachers can be formed in 1050 different ways.
