Let A be the set of all sequences of 0s 1s and 2s of length

Let A be the set of all sequences of 0\'s, 1\'s, and 2\'s of length 12. How many elements are there in A? How many elements of A have exactly six 0\'s and six 1\'s? How many elements of A have exactly three 0\'s. four 1\'s and five two\'s?

Solution

a)
(3^12)= 531441
b)
12/(!6)(!6)=12x11x10x9x8x7x!6/!6*!6 = 12x11x10x9x8x7/[6x5x4x3x2]=924
c)
(12! / (3!*4!*5!)) = 27720