Question

find the no. of words that can be formed from the letters of the word MALAYALAM. how? How many of these arrangements start with Y?

Answer 1

Given:

The given word is MALAYALAM

To find:

(i)We have to find the number of words that can be formed from the letters of the word MALAYALAM

(ii)We have to find the number of words that  can be formed from the letters of the word MALAYALAM,which starts with Y

Solution:

Total number of letters = 9

Number of A's in the word = 4

Number of L's in the word = 2

Number of M's in the word = 2

Number of Y's in the word = 1

From the concept of permutations and combinations,

Number of words formed from the letters of the word MALAYALAM = $\frac{9!}{4!2!2!1!}$

                                                                                                                  = $\frac{362880}{96}$

                                                                                                                  = 3780

∴The total number of words that can be formed from the letters of the word MALAYALAM = 3780

First let us fix the letter Y in initial position  Y_ _ _ _ _ _ _ _

After fixing Y there are 8 placws left over

So number of words starting with Y =  $\frac{8!}{4!2!2!}$

                                                           =  $\frac{40320}{96}$

                                                           =  420

∴The number of words that can be formed the letters of the word MALAYALAM starting with Y = 420