The number of ways the word MOSHOESHOE can be rearranged, if the letter M must always begin a word is 75,600 ways
Given:
MOSHOESHOE
n = total number of letters = 10
a = number of times O appears = 3
b = number of times S appears = 2
c = number of times E appears = 2
d = number of times H appears = 2
number of ways the word can be rearranged if M must always begin a word
= n! / (a! b! c! d!)
= 10! / (3!, 2!, 2!, 2!)
= (10 × 9 × 8 × 7 × 6 × 5 × 4× 3 × 2 × 1) / (3 × 2 × 1, 2 × 1, 2 × 1, 2 × 1)
= 3,628,800 / (6 × 2 × 2 × 2)
= 3,628,800 / 48
= 75,600 ways
Therefore, the number of ways the word can be rearranged if M must always begin a word is 75,600 ways
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