For the post of 5 teachers, there are 23 applicants, 2 spots are reserved for SC candidates and there are 7 SC candidates among the applicants. In how many ways can the selection be made?

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Solution

There are $7 S C$ candidates and $16$ other candidates. We have to select $2$ out of $7 S C$ candidates and $3$ out of $16$ other candidates. This can be done in $7_{C_{2}} \times 16_{C_{3}}$ ways.

The number of ways of making the selection = $7_{C_{2}} \times 16_{C_{3}} = 11760$

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For the post of 5 teachers, there are 23 applicants, 2 spots are reserved for SC candidates and there are 7 SC candidates among the applicants. In how many ways can the selection be made?

There are 7 SC candidates and 16 other candidates. We have to select 2 out of 7 SC candidates and 3 out of 16 other candidates. This can be done in 7C2×16C3 ways.The number of ways of making the selection = 7C2×16C3=11760

There are $7 S C$ candidates and $16$ other candidates. We have to select $2$ out of $7 S C$ candidates and $3$ out of $16$ other candidates. This can be done in $7_{C_{2}} \times 16_{C_{3}}$ ways.

The number of ways of making the selection = $7_{C_{2}} \times 16_{C_{3}} = 11760$