The number of words from the letters of the word ‘BHARAT’ in which

1.	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» Option : (B) We have, 6 objects {B}, {H}, {A}, {R}, {A}, {T} and there are 2 A's. So, the number of words that can be formed out of the letters of the word ‘BHARAT’ is = \(\frac{6!}{2!}\) = 360 The number of words that can be formed out of the letters of the word ‘BHARAT’ is in which {B} and {H} come together is = 5! = 120. [considering {BH} as a single object] Hence, The number of words from the letters of the word ‘BHARAT’ in which B and H will never come together, is = (360 – 120) = 240.

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»

Option : (B)

We have,

6 objects {B}, {H}, {A}, {R}, {A}, {T} and there are 2 A's.

So, the number of words that can be formed out of the letters of the word ‘BHARAT’ is

= \(\frac{6!}{2!}\)

= 360

The number of words that can be formed out of the letters of the word ‘BHARAT’ is in which {B} and {H} come together is = 5!

= 120.

[considering {BH} as a single object]

Hence,

The number of words from the letters of the word ‘BHARAT’ in which B and H will never come together, is = (360 – 120)

= 240.