Class 11

Math

Algebra

Permutations and Combinations

Five-letter words are to be formed out of the letters of the word INFINITESIMAL. What is their number?

13 letters ($4I,2N,7$ diff.) 9 types

All diff. $_{9}C_{5}.5!=15120$

2 alike, 3 diff. $_{2}C_{1}._{8}C_{3}.2!5! =6720$

2 alike, 2 alike, 1 diff. $_{2}C_{2}._{7}C_{1}.2!2!5! =210$.

3 alike, 2 diff. $_{1}C_{1}._{8}C_{2}.3!5! =560$

3 alike, 2 alike $_{1}C_{1}._{1}C_{1}.3!2!5! =10$

4 alike, 1 diff. $_{1}C_{1}._{8}C_{1}.4!5! =40$

Total $=22660$.