Questions: Suppose we want to choose 7 objects, without replacement, from 12 distinct objects. (If necessary, consult a list of formulas.) (a) How many ways can this be done, If the order of the choices matters? (b) How many ways can this be done, if the order of the choices does not matter?

Suppose we want to choose 7 objects, without replacement, from 12 distinct objects.
(If necessary, consult a list of formulas.)
(a) How many ways can this be done, If the order of the choices matters?

(b) How many ways can this be done, if the order of the choices does not matter?

Transcript text: Suppose we want to choose 7 objects, without replacement, from 12 distinct objects. (If necessary, consult a list of formulas.) (a) How many ways can this be done, If the order of the choices matters? $\square$ (b) How many ways can this be done, if the order of the choices does not matter? $\square$

Solution

Solution Steps

Step 1: Calculating the number of combinations

To calculate the number of combinations (order does not matter) of choosing 7 items from 12 distinct items, we use the formula: $$ C(n, r) = \frac{n!}{r!(n-r)!} $$ Substituting the given values, we get: $$ C(12, 7) = \frac{12!}{7!(12-7)!} = 792 $$

Step 2: Calculating the number of permutations

To calculate the number of permutations (order matters) of choosing 7 items from 12 distinct items, we use the formula: $$ P(n, r) = \frac{n!}{(n-r)!} $$ Substituting the given values, we get: $$ P(12, 7) = \frac{12!}{(12-7)!} = 3991680 $$

Final Answer:

The number of ways to choose 7 items from 12 distinct items, without replacement, is 792 if the order of the choices does not matter (combinations), and 3991680 if the order of the choices matters (permutations).

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!