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Q.

3 letters are to be posted in 5 letter boxes in a port of the town. If all the letters are not posted in the same letter box, the number of ways of posting is $k,$ then sum of the digits of $k =$ ____

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answer is 6.

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Detailed Solution

The number of ways of posting $=^{5} p_{3}$

$^{5} p_{3} = k$

$5 \times 4 \times 3 = k$

$k = 60$

Sum of digits of $k = 6 + 0 = 6$

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