1. Tardigrade
  2. Question
  3. Mathematics
  4. The number of ways of selecting 4 letters out of the letters of the word MINIMAL is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The number of ways of selecting 4 letters out of the letters of the word MINIMAL is

Permutations and Combinations

Solution:

Letters of the word, M I N I M A L are ( $M$, M) $(I, I), A, N, L$
We can select 4 letters from letters of the word MINIMAL as follows:
Case 1 All letters are distinct.
This can be done in ${ }^5 C_4=5$ ways
Case 2 Exactly two letters are identical.
We can choose two identical letters in ${ }^2 C_1$ ways and two remaining distinct letters in ${ }^4 C_2=6$ ways
$\therefore$ In this case the selection can be made in (2) $(6)=12$ ways.
Case 3 Two pairs of identical letters are selected.
This can be done in ${ }^2 C_2=1$ way
$\therefore$ two number of ways
$=5+12+1=17 $