BRILLIANT

Level 2

How many "words" can the letters of "BRILLIANT" be formed into if every letter is used once? The answer is a five-digit number. Find the sum of the digits of the number.

Ex: ("RIILLANTB", "ILLIANTRB" are defined as "words".)


The answer is 18.

Bob Yang by Bob Yang , 23, USA

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1 solution

Ashish Menon
May 9, 2016

The number of words that can be formed = 9 ! 2 ! × 2 ! \dfrac{9!}{2! × 2!} because there are 9 alphabets and L and I repeat twice. So, the number of words that can be formed = 90720 90720 . So, the sum of the digits = 9 + 0 + 7 + 2 + 0 = 18 9 + 0 + 7 + 2 + 0 = \boxed{18} .

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