Answer:
A. 7560
Step-by-step 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.
