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  4. The number of arrangements of the letters of the word BANANA in which the two N’s do not appear adjacently is

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Q. The number of arrangements of the letters of the word BANANA in which the two N’s do not appear adjacently is

Permutations and Combinations

Solution:

B A N A N A
First arrange BAAA in $\frac{4 !}{3 !}=4$ ways
Now 5 gaps available to be filled with 2 numbers
$\therefore 4 \times{ }^5 C _2=40$