The number of arrangements of the letters of the word BANANA in which

1.	The number of arrangements of the letters of the word BANANA in which two N’s do not appear adjacently is (A) 80(B) 60(C) 40(D) 100
Answer» (C) 40 Arrange B, A, A, A in \(\frac{4!}{3!}\) ways. These four letters create 5 gaps in which 2 N are to be filled, this can be done in 5C2 ways, we do not permute those 2N as they are identical. ∴ Required number = \(\frac{4!}{3!}\times\,^5C_2=40\)

The number of arrangements of the letters of the word BANANA in which two N’s do not appear adjacently is (A) 80(B) 60(C) 40(D) 100

Answer»

(C) 40

Arrange B, A, A, A in \(\frac{4!}{3!}\) ways.

These four letters create 5 gaps in which 2 N are to be filled, this can be done in 5C2 ways, we do not permute those 2N as they are identical.

∴ Required number = \(\frac{4!}{3!}\times\,^5C_2=40\)