# Using Permutation Solve the FollowingHow many different seven-person committees can be formed each containing three female members from an available set of 20 females and four male members from a...

Using Permutation Solve the FollowingHow many different seven-person committees can be formed each containing three female members from an available set of 20 females and four male members from a set of 30 males?

sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to rememeber factorial formula of combinations such that:

`C_n^k = (n!)/(k!(n-k)!)`

You need to form seven person committees consisting of 3 females from a total of 20 and 4 males from a total of 30.

You need to express how many possible groups of 3 females may be formed from a total of 20 females, using factorial formula of combinatons such that:

`C_20^3 = (20!)/(3!(20-3)!) =gt C_20^3 = (20!)/(3!*17!)`

`C_20^3 = (17!18*19*20)/(3!*17!)`

`C_20^3 = (18*19*20)/(1*2*3)`

`C_20^3 = 3*19*20 = 1140 `

You need to express how many possible groups of 4 males may be formed from a total of 30 males, using factorial formula of combinatons such that:

`C_30^4 = (30!)/(4!(30-4)!) =gt C_30^4 = (30!)/(4!26!)`

`C_30^4 = (26!27*28*29*30)/(4!26!)`

`C_30^4 = (27*28*29*30)/(1*2*3*4)`

`C_30^4 = (27*7*29*5)`

`C_30^4 = 27405`

Hence, there may be formed `C_20^3*C_30^4 = 1140*27405=31241700`  different seven-person committees consiting of 3 females out of total of 20 and 4 males out of total of 30.