Q.
The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word 'EXAMINATION' is __________.
Given 8
Solution:
$N \to 2, A \to 2, I \to 2, E, X, M, T, O \to 1$
Category Selection Arrangement 2alikeof one kind and 2 alike of other kind $^{3}C_{2} = 3$ $3\times \frac{4!}{2!\,2!} = 18$ 2 alike and 2 different $^{3}C_{1} \times ^{7}C_{2}$ $^{3}C_{1}\times^{7}C_{2}\times \frac{4!}{2!} = 756$ All 4 different $^{8}C_{4} $ $^{8}C_{4} \times 4! = 1680$
Total $= 2454$
| Category | Selection | Arrangement |
|---|---|---|
| 2alikeof one kind and 2 alike of other kind | $^{3}C_{2} = 3$ | $3\times \frac{4!}{2!\,2!} = 18$ |
| 2 alike and 2 different | $^{3}C_{1} \times ^{7}C_{2}$ | $^{3}C_{1}\times^{7}C_{2}\times \frac{4!}{2!} = 756$ |
| All 4 different | $^{8}C_{4} $ | $^{8}C_{4} \times 4! = 1680$ |