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

Answer 1

Answer: (B)

($240$)

Given word is BHARAT.
Total number of letters $=6$, In which 'A' repeated twice.
Number of different words formed $=\frac{6!}{2!}$

$=6\times 5\times 4\times 3$

$=360$

Number of words in which the letters B and H are always together = $2\times \frac{5!}{2!}$
Here, B and H are together consider as a bunch, so we get $5$ letters and again B and H can be interchanged $2!$ ways in them selves.
Thus, $2\times \frac{5!}{2!}=5\times 4\times 3\times 2$
$=120$

$\therefore$ Number of words in which the letters B and H are never together $=360-120=240$