11,How many different committees can be formed from 10 teachers and 38 students if the committee consists of 4 teachers and 3 students?The committee of 7 members can be selected in different ways.Help me solve thisView an example Get more help -

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Solution

Let C(n, r) denotes the combination of n object selecting r and it is defined as

[tex]C(n,r)=\frac{n!}{(n-r)!r!}[/tex]

The number of ways will be

[tex]\begin{gathered} Number\text{ }Of\text{ }Ways=C(10,4)\times C(38,3) \\ \\ Number\text{ }Of\text{ }Ways=\frac{10\times9\times8\times7\times6!}{6!4!}\times\frac{38\times37\times36\times35!}{35!3!} \\ \\ Number\text{ }Of\text{ }Ways=210\times8436 \\ \\ Number\text{ }Of\text{ }Ways=1771560 \end{gathered}[/tex]