How many words can be made from letters of word BHARAT in which B and H never come together

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Gujarati

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6.Permutation and Combination

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How many words can be made from the letters of the word $BHARAT$ in which $ B $ and $H$ never come together

A

$360$

B

$300$

C

$240$

D

$120$

(IIT-1977)

Solution

(c) The total number of words $ = \frac{{6\;!}}{{2\;!}} = 360$.

The number of words in which $BH$ come together are

$\frac{{5\;!}}{{2\;!}} \times 2\;! = 120$.

Hence required number of ways in which $B$ and $H$ never came together are $360 – 120 = 240$.

Standard 11

Mathematics

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