Question help :

Question

1.when it comes to solving counting problems,

how would you know when to use (4³powers) (factorials !),

_{or n}P_r(permutations) ?

Answer 1

Permutations involve factorials. nPr = n!/r! = for example 5 choose 2 = 5!/2! = 5x4x3x2!/2! = 5x4x3 = 60 outcomes. n! = nx(n-1)x(n-2)....x1. For combinations, there's more factorials, but a smaller result: nCr = n!/r!(n-r)!

exponents are "with replacement" problems. roll a die with 6 sides 3 times, chances of getting 3 ones or 3 of any outcome is (1/6)^3=(1/6)(1/6)(1/6 = 1/216

Or there's 6 marbles in a bag. You randomly pick one, replace it, pick again, replace it and pick a marble a 3rd time. Odds of 3 of a kind, if each marble is a different color is 1/216. Flip a coin twice. Odds of 2 tails is (1/2)^2 = 1/4

Answer 2

Powers and factorials are only notations. They compact the information.

Permutations are used when order makes a difference, e.g. awarding first, second, place in a contest.

Combination is used when order does not make a difference, e.g. how many 5 person teams can be made from a pool of 10 players.