The number of words from the letters of the word 'BHARAT' in which B and H will never come together,

Question:

The number of words from the letters of the word 'BHARAT' in which B and H will never come together, is

(a) 360

(b) 240

(c) 120

(d) none of these.

Solution:

(b) 240

Total number of words that can be formed of the letters of the word BHARAT $=\frac{6 !}{2 !}$

= 360

Number of words in which the letters $\mathrm{B}$ and $\mathrm{H}$ are always together $=2 \times \frac{5 !}{2 !}$

= 120

$\therefore$ Number of words in which the letters $\mathrm{B}$ and $\mathrm{H}$ are never together $=360-120$

= 240

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