Tamil Nadu Board of Secondary EducationHSC Science Class 11

How many different selections of 5 books can be made from 12 different books if, Two particular books are always selected? - Mathematics

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Sum

How many different selections of 5 books can be made from 12 different books if, Two particular books are always selected?

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Solution

Total number of books = 12

Number of books to be selected = 5

Given Two books are always selected.

Remaining number of books to be selected = 3

The number of ways of selecting the remaining 3 books from the remaining 10 books = 10C

= `(10!)/(3! xx (10 - 3)!)`

= `(10!)/(3! xx 7!)`

= `(10 xx 9 xx 8 xx 7!)/(3! xx 7!)`

= `(10 xx 9 xx 8)/(3!)`

= `(10 xx 9 xx 8)/(3 xx 2 xx 1)`

= 5 × 3 × 8

= 120 ways

Concept: Combinations
  Is there an error in this question or solution?
Chapter 4: Combinatorics and Mathematical Induction - Exercise 4.3 [Page 187]

APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 11th Mathematics Volume 1 and 2 Answers Guide
Chapter 4 Combinatorics and Mathematical Induction
Exercise 4.3 | Q 13. (i) | Page 187

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