a In how many different ways can the letters in COELUROSAURA

a) In how many different ways can the letters in COELUROSAURAVUS be arranged?

b) In how many different ways can the letters in COELUROSAURAVUS be arranged if the first letter must be a V and the last letter must be an O?

V is first place and O is in last then the total arrangements = (1! 2!)/2! = 1 way

Remaning letters 12 letters in 13 places are arranged 13P12 ways

Again I can not leave my answer as 13P12 how do I finish the problem?

Solution

A. You can use a calculator in this case. The answer is very big.

The expression

15! / [2!3!2!2!2!] = 1.3621608*10^10 [ANSWER]

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Note that that last 2 letters are fixed.

Thus, you need to permute the 13 letters in the middle the same way you did above.

Thus,

13! / [3!2!2!2!] = 129,729,600 [ANSWER]