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प्रश्न
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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उत्तर
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.
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