Query about question "In how many different ways can..." [768]

[user10997]

https://www.gregmat.com/problems/quant?problem=in-how-many-different-ways-can

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Can someone explain for me why it is not 2 x 4 x 3 x 2 x 1?

Why times 3 and times 5?

because :

• there are two vowels I and E
• after I and E there are only 4 ways x 3 ways x 2 ways x 1 way to reorganize the letter

[Kweku]

@user10997

Can someone explain for me why it is not 2 x 4 x 3 x 2 x 1?

@user10997

there are two vowels I and E

@user10997

after I and E there are only 4 ways x 3 ways x 2 ways x 1 way to reorganize the letter

You’ll be solving a different question, specifically, You’ll be solving for EMPIR or MPIRE or some iteration with one ‘E’ letter.

@user10997

Why times 3

Because there are three vowels E, E, I

@user10997

and times 5?

We have 5 choices (3 from M,P and R and 2 from what’s left after choosing 1 from E,E,I)

3 × 5!/2!

We divide by 2! to take care of the double Es