M7MBA wrote: ↑

Sun Jan 03, 2021 11:11 am

How many 4-letter words can be formed using the alphabets of the word ENGLISH, if it is given that the 4-letter word contains alphabets G and L and repetition of alphabets are not allowed?

A. 60
B. 120
C. 180
D. 200
E. 240

Answer: E

Source: e-GMAT

Take the task of creating 4-letter words and break it into stages.

Stage 1: Select 2 letters from E, N, I, S, H
Since the order in which we select the two letters does not matter (yet!!), we can use combinations.
We can select 2 letters 5 letters in 5C2 ways (10 ways)
So, we can complete stage 1 in 10 ways

ASIDE: If anyone is interested, we have a video on calculating combinations (like 5C2) in your head below

Stage 2: Combine G and L with the two letters you chose in stage 1, and then arrange those 4 letters
We can arrange n objects in n! ways
So, we can arrange the 4 letters in 4! ways (= 24 ways)
We can complete stage 2 in 24 ways

By the Fundamental Counting Principle (FCP), we can complete the two stages (and thus create 4-letter words) in (10)(24) ways (= 240 ways)

Answer: E