The selection of members of the committee is an illustration of combination.
The number of ways of selection is 765
The given parameters are:
[tex]\mathbf{Men = 10}[/tex]
[tex]\mathbf{Women = 6}[/tex]
At least 5 women means that:
- There are 5 women and 1 man in the committee or
- There are 6 women and no man in the committee
So, the possible selection is:
[tex]\mathbf{Selection = ^6C_5 \times ^{10}C_3 + ^6C_6 \times ^{10}C_2}[/tex]
Apply combination formula
[tex]\mathbf{Selection = \frac{6!}{5!1!} \times \frac{10!}{7!3!} + \frac{6!}{6!0!} \times \frac{10!}{8!2!}}[/tex]
[tex]\mathbf{Selection = 6 \times 120 + 1 \times 45}[/tex]
[tex]\mathbf{Selection = 720 + 45}[/tex]
[tex]\mathbf{Selection = 765}[/tex]
Hence, the number of ways of selection is 765
Read more about selections and combinations at:
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