Question 12 of 14, Step 1 of 1
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Tabitha is packing for a trip. She has 16 pairs of jeans. If she has room to pack 8 pairs, how many ways - can she choose which jeans to take?

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Step 1 ：Calculate the number of combinations using the formula C(n, r) = n! / (r!(n-r)!)

Step 2 ：Substitute n = 16 and r = 8 into the formula

Step 3 ：Simplify the expression C(16, 8) = 16! / (8! * 8!)

Step 4 ：Calculate the factorial values: 16! = 16 * 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8! and 8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

Step 5 ：Substitute the factorial values back into the formula

Step 6 ：Simplify further to get C(16, 8) = (16 * 15 * 14 * 13 * 12 * 11 * 10 * 9) / (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)

Step 7 ：Calculate the numerator and denominator separately

Step 8 ：Numerator = 16 * 15 * 14 * 13 * 12 * 11 * 10 * 9 = 65318400

Step 9 ：Denominator = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40320

Step 10 ：Calculate the final result: C(16, 8) = 65318400 / 40320 = 1624