Linear Arrangements

Probability Level pending

How many different arrangements are there of the letters B, C, D, E, F and G for which B is before C and C is before D?

The answer is 120.

1 solution

Andy Hayes
Jan 4, 2017

There are 6 possible placements of the letters. Since B, C, and D are always in that order, choose 3 placements for them. There are $\binom{6}{3}$ ways to do this. Then, there are $3!$ ways to permute the remaining letters among the remaining 3 placements. The number of possible arrangements is:

$3!\binom{6}{3}=\boxed{120}.$

Linear Arrangements

The answer is 120.

1 solution

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