Question

How many ways can six of the letters of the word 'PALINDROME' be selected and written in a row if the first two letters must be M and E in any order?

Answer 1

BY permutation, There are 90 ways by which the arrangement of  'PALINDROME' takes place.

According to the statement

we have given that the word 'PALINDROME' and we have to find that the in how much ways this word can be arranged.

So, For this purpose, we use the permutation here

So, A permutation is a mathematical technique that determines the number of possible arrangements.

The word given is:

'PALINDROME' this contain 10 words and given 2 words M and E are in any order.

So, Permutation takes place with $P^{10} _{2}$.

So,

$P^{10} _{2}$

Now solve this then

$P^{10} _{2} = \frac{10!}{(10 -2) !}$

And

$P^{10} _{2} = \frac{10!}{(8) !}$

$P^{10} _{2} = \frac{10*9*8*7*6*5*4*3*2*1}{(8*7*6*5*4*3*2*1) !}$

And then after take common from them and cancel it the equation become

$P^{10} _{2} = 10*9$

$P^{10} _{2} = 90$

90 ways are comes as the output.

So, BY permutation, There are 90 ways by which the arrangement of  'PALINDROME' takes place.

Learn more about permutation here

brainly.com/question/11732255

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