Suppose we want to choose 6 letters, without replacement, from 10 distinct letters.(If necessary, consult a list of formulas.)(a) If the order of the choices is relevant, how many ways can this be done?(b) If the order of the choices is not relevant, how many ways can this be done?
Question
Suppose we want to choose 6 letters, without replacement, from 10 distinct letters.(If necessary, consult a list of formulas.)(a) If the order of the choices is relevant, how many ways can this be done?(b) If the order of the choices is not relevant, how many ways can this be done?
Solution
(a) If the order of the choices is relevant, we use the formula for permutations of n items taken r at a time, which is nPr = n! / (n-r)!. Here, n is the total number of items, and r is the number of items to choose. So, we have 10P6 = 10! / (10-6)! = 151,200 ways.
(b) If the order of the choices is not relevant, we use the formula for combinations of n items taken r at a time, which is nCr = n! / [r!(n-r)!]. So, we have 10C6 = 10! / [6!(10-6)!] = 210 ways.
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