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