# Five students are selected from 11. How many ways can these students be selected if two specified students are selected? - Mathematics and Statistics

Sum

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

#### 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.

Concept: Properties of Combinations
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.7 | Q 15. (a) | Page 90