Find the number of arrangements of letters in the word MUMBAI so that

1.	Find the number of arrangements of letters in the word MUMBAI so that the letter B is always next to A.
Answer» There are 6 letters in the word MUMBAI. These letters are to be arranged in such a way that ‘B’ is always next to ‘A’. Let us consider AB as one unit. This unit with the other 4 letters in which ‘M’ repeats twice is to be arranged. ∴ Required number of arrangements = \(\frac{5!}{2!}\) = \(\frac{5\times4\times3\times2}{2!}\) = 60

Find the number of arrangements of letters in the word MUMBAI so that the letter B is always next to A.

Answer»

There are 6 letters in the word MUMBAI.

These letters are to be arranged in such a way that ‘B’ is always next to ‘A’.

Let us consider AB as one unit.

This unit with the other 4 letters in which ‘M’ repeats twice is to be arranged.

∴ Required number of arrangements = \(\frac{5!}{2!}\) = \(\frac{5\times4\times3\times2}{2!}\) = 60