Question

how many different permutations can you make with the letters in the word seventeen A.7560 B.15120 C 17! D.3780​

Answer 1

A. 7560

Explanation:

There are nine letters in the word SEVENTEEN:

1 S

4 Es

1 V

2 Ns

1 T

Possible positions:

For the S, any one of the nine positions. That's ⁹C₁ positions.

For the Es, any four of the remaining eight positions. That's ⁸C₄ positions.

For the V, any one of the remaining four positions. That's ⁴C₁ positions.

For the N, any two of the remaining three positions. That's ³C₂ positions.

For the T, only one way to fill the last position. That's ¹C₁ position.

Total number of positions

= ⁹C₁ × ⁸C₄ × ⁴C₁ × ³C₂ × ¹C₁ = 9 × 70 × 4 × 3 × 1

= 7560

There are 7560 permutations of the letters in the word SEVENTEEN.