Maharashtra State BoardHSC Science (General) 11th
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You have 2 identical books on English, 3 identical books on Hindi, and 4 identical books on Mathematics. Find the number of distinct ways of arranging them on a shelf - Mathematics and Statistics

Sum

You have 2 identical books on English, 3 identical books on Hindi, and 4 identical books on Mathematics. Find the number of distinct ways of arranging them on a shelf

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Solution

2 identical books on English, i.e., p = 2

3 identical books on Hindi, i.e., q = 3

4 identical books on Mathematics, i.e., r = 4

Total number of books is n = 2 + 3 + 4 = 9

∴ the number of distinct ways of arrangement of books on a shelf is

`("n"!)/("p"!"q"!"r"!)`

= `(9!)/(2!3!4!)`

= `(9 xx 8 xx 7 xx 6 xx 5 xx 4!)/(3 xx 2 xx 1 xx 2 xx 1 xx 4!)`

= 9 × 4 × 7 × 5

= 1260.

Concept: Concept of Permutations - Permutations When Some Objects Are Identical
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 3 Permutations and Combination
Exercise 3.4 | Q 2 | Page 57
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