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Five students are selected from 11. How many ways can these students be selected if two specified students are selected?

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#### Solution

Number of students = 11

Number of students to be selected = 5

Here, 2 specified students are included.

So, we need to select 3 more students from the remaining 9 students.

This can be done in:

= `""^9"C"_3`

= `(9 xx 8 xx 7)/(3 xx 2 xx 1)`

= 84 ways

∴ Number of required selections

= 84 × 1 × 1

= 84

Thus, 84 selections. can be made such that 2 specified students are included.

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