Question

the letters of the word MUMMY are placed at randomin a row,the chance that the letters at the extremes are M andY

Answer 1

HELLO FRIEND HERE IS YOUR ANSWER,,,,,,

Let us take the total number of obtaining the placement of 5 total letters in a complete row which are having 3 letters as the same

Here permutations and combinations are applied to obtain the answer,,,,

STEP BY STEP SOLUTION::;

$M = \frac{5!}{3!} \\ \\ \\ = > \frac{5 \times 4 \times 3 \times 2 \times 1}{3 \times 2 \times 1} \\ \\ \\ = > 20$

Therefore, to find a number of total ways in which "M" is present at the extremes, we can conclude that, the remaining three letters, that is, "M" , "U" , "Y" , can get into the place in between them and in $^3$P$_3$ , that is , in a total of "6 ways" it can be placed.....

FINDING THE TOTAL PROBABILITY,,, we get

Therefore,,, P$_6$ = $\frac{6}{20}$

Final answer,,,

P$_6$ = $\frac{3}{10}$

Which is the required solution for this type of query.

HOPE IT HELPS YOU AND CLEARS YOUR DOUBTS FOR USING PERMUTATIONS AND COMBINATIONS ALONG WITH PROBABILITY!!!!!