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Five students are selected from 11. How many ways can these students be selected if two specified students are not selected?

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#### Solution

Number of students = 11

Number of students to be selected = 5

Here, 2 specified students are not included.

So, we need to select 5 students from the remaining 9 students.

This can be done in:

= `""^9"C"_5`

= `(9 xx 8 xx 7 xx 6)/(4 xx 3 xx 2 xx 1)`

= 126 ways

Thus, 126 selections can be made such that 2 specified students are not included.

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