[Math] In how many ways can the 26 letters in the alphabet…

Question

In how many ways can the 26 letters in the alphabet be arranged so b be somewhere to the left of e?

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Basically, all the permutations in which the letter 'b' comes before the letter 'e'

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How can I do this?

Answer 1

There are $26!$ different arrangements, in half of which 'b' comes before 'e'.

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Alternatively, you can multiply the following:

• Number of ways to choose places for 'b' and 'e', which is $\binom{26}{2}$
• Number of ways to arrange the remaining letters, which is $(26-2)!$