Question

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

• A. 16
• B. 17
• C. 18
• D. 20

Answer 1

Answer: (B)

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
$=5+12+1=17$