Just think of how many possibilities you have for each digit. 10x9x8x7x6x5x4x3x2 or 10 factorial is 3 628 800.
BASKETBALL = 10 letters B=2 A=2 S=1 K=1 E=1 T=1 L=2 Number of permutations = 10! /2!2!2! = 10x9x8x7x6x5x4x3x2 / 2x2x2 =3,628,800 / 8 =453,600