# 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...

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### 1 Answer

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.**