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

(a) two specified students are selected?

(b) two specified students are not selected?

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Best answer

5 students are to be selected from 11 students.

(a) When 2 specified students are included, then remaining 3 students can be selected from (11 – 2) = 9 students. ∴ Number of ways of selecting 3 students from 9 students = 9C3

∴ Selection of students is done in 84 ways when 2 specified students are included.

(b) When 2 specified students are not included, then 5 students can be selected from the remaining (11 – 2) = 9 students.

 ∴ Number of ways of selecting 5 students from 9 students = 9C5

 = 126

∴ Selection of students is done in 126 ways when 2 specified students are not included.

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