Question 26

With eleven distinct consonants and five distinct vowels, how many distinct six letter words can be formed if middle two positions are occupied by vowels (may be repeated) and first two and last two positions are occupied by consonants (all distinct)?

Solution

Let the six-letter word be ABCDEF

Number of possibilities for A = 11, B = 10, C = 5, D=5, E = 9, F = 8

Required number of ways = 11*10*5*5*9*8 = 198000

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