The number of 5-letter words that can be formed by using the letters of the word SARANAM is
The number of 5-letter words that can be formed by using the letters of the word SARANAM is
1120
6720
480
720
Solution
There are 7 letters in the word 'SARANAM' of which there are $3 \mathrm{~A}$ and all other are distinct.
The five letter words may consist of
(i) all different letters (using S, A, R, N, M)
$\therefore$ Required words
$
=5 !=120
$
(ii) 2 alike and other different
(using $2 \mathrm{~A}$ and 3 other)
$\therefore$ Required words
$
={ }^4 C_3 \times \frac{5 !}{2 !}=4 \times \frac{120}{2}=240
$
(iii) 3 alike and other different (using 3A and 2 other)
$\therefore$ Required words $={ }^4 C_2 \times \frac{5 !}{3 !}=\frac{4 \times 3}{2 \times 1} \times \frac{120}{6}=120$
$\therefore$ Total words $=120+240+120=480$