Question

find the number of arrangement of the letters of word MATHEMATICS taken four letter at a time​

Answer 1

hey dude !!!

=>> math ,them , mats etc ..

hope this helps you

Answer 2

Answer:

2454

Step-by-step explanation:

M - 2 times

A - 2 times

T - 2 times

H

E

I

C

S

Taking 4 at a time:

Case 1. Taking all different letters.

8 different letters

So, selecting 4 out of 8 = 8C4

and with arrangements = 8C4 × 4!

= 8P4 =1680

Case 2. Taking 3 different letters with one repeating.

8 letters in which we'll have to take 7 different, and 1 repeating (along M, A or T)

Selecting 1 different out of 3 = 3C1

and selecting 2 letters out of 7 different letters = 7C2

Now Total with arrangements = 3C1*7C2*(4!/2!)

= 756

Case 3. Taking 2 repeating letters.

So selecting 2 letters or of 3 repeating letters = 3C2

Total with Arrangements = 3C2*(4!/(2!*2!))

= 18

So, Finally Total number of arrangements = [8P4] + [3C1*7C2*(4!/2!)] + [3C2*(4!/(2!*2!))]

= 1680 + 756 + 18

= 2454