Theory question 101
Permutations and CombinationsIf 9Cx = 4[7Cx−1], find the values of x.
Show the model answer
Model answer
9!/(x!(9 − x)!) = 4 × 7!/((x − 1)!(8 − x)!).
Cancel 7!, (x − 1)! and (8 − x)!: 72/(x(9 − x)) = 4.
x(9 − x) = 18, so x² − 9x + 18 = 0, (x − 3)(x − 6) = 0.
x = 3 or x = 6.
Explanation
Write both sides in factorials and cancel the common parts.