Simple Arrangements & Selections Combinations & Permutations A permutation of n distinct objects is an arrangement , or ordering , of the n objects. An r -permutation of n distinct objects is an arrangement using r of the n objects.
= n(n - 1) . . . (n - (r - 1)) (n - r)!/(n - r)!
= n!/(n - r)!
1. pick the r elements to be ordered: C(n, r)
2. Order the r elements: P(r, r) = r!
How many ways can 7 women & 3 men be arranged in a row, if the 3 men must be adjacent?
How many ways are there to arrange the alphabet so that there are exactly 5 letters between a & b?
How many 6-digit numbers without repetition are there so that the digits are nonzero, and 1 & 2 do not appear consecutively?
P(9, 6) - C(5, 1)(2)P(6, 4) ways to do this.
How many ways are there to arrange the letters in the word MISSISSIPPI?
Thus, there are
C(7, 2)C(4, 2) + C(7, 3)C(4, 1) + C(7, 4)C(4, 0) such committees.