Question

Find the number of words that can be formed by selecting 5 letters of the word independent

Answer 1

Case 1 out of 5 3 are alike of one kind and 2 are different =2C1×5C2×5!÷3!=400

Case 2 3 are alike of one kind and 2 of other kind = 2C1×2C1×5!÷3!2!=40

CASE 3 2 are alike of one kind and two are alike of other kind and one is different =3C2×4C1×5!÷2!2!=3C260

CASE 4 2 are alike 3 are different =3C2×5C3×5!÷2!=1800

CASE 5 all are different =6!=720

Total = 400+40+360+720+1800

=3320