Respuesta :
The question provides that there are 15 boys and 10 girls from which a committee of 3 boys and 2 girls is to be formed.
QUESTION I
The number of ways the committee can be chosen when there is no restriction can be calculated as follows:
Number of ways to pick 3 boys from 15:
[tex]15C3[/tex]Number of ways to pick 2 girls from 10:
[tex]10C2[/tex]Therefore, the number of ways the choice can be made will be:
[tex]\begin{gathered} \Rightarrow15C3\times10C2=455\times45 \\ =20475\text{ ways} \end{gathered}[/tex]QUESTION II
If a particular boy is included, the number of choices will then become:
[tex]14C2[/tex]Therefore, the number of ways the choice can be made will be:
[tex]\begin{gathered} \Rightarrow14C2\times10C2=91\times45 \\ =4095\text{ ways} \end{gathered}[/tex]QUESTION III
If a particular girl is excluded, the number of choices will be:
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