Question

How many arrangements of the seven letters in the word SYSTEMS have the E occurring somewhere before the M? How many arrangements have the E somewhere before the M and the three Ss grouped consecutively?

Answer 1

Answer: 720ways, 24ways

Explanation:

Given the seven letter words "SYSTEMS", if E is always occurring before M it means E and M will always be together therefore they letter 'EM' will be taken as an entity to five us 6letters i.e SYST(EM)S.

This can then be arranged in 6!ways

6! = 6×5×4×3×2×1 = 720ways

Similarly, if the E somewhere before the M and the three Ss grouped consecutively, this means E and M must always be together as well as the Ss to give (SSS)YT(EM).

This means that the letters in the bracket can be taken as an entity to give a total of 4 entities. This can them be arranged in 4! ways.

4! = 4×3×2×1

4! = 24ways