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Sagot :
Given:
There are a group of ‘10’ women and ‘10’ men
We will find the number of ways to choose a committee of 5 men and 4 women
We will use the combinations to solve the problem:
The general formula of the combinations is:
[tex]^nC_r=\frac{n!}{(n-r)!\cdot r!}[/tex]First, we will find the number of ways to choose 5 men from 10 men
So, the number of ways =
[tex]^{10}C_5=\frac{10!}{(10-5)!\cdot5!}=\frac{10!}{5!\cdot5!}=252[/tex]Second, we will find the number of ways to choose 4 women from 10 women
So, the number of ways =
[tex]^{10}C_4=\frac{10!}{(10-4)!\cdot4!}=\frac{10!}{6!\cdot4!}=210[/tex]Finally, the total number of ways will be =
[tex]^{10}C_5\times^{10}C_4=252\times210=52,920[/tex]So, the answer will be 52,920
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