Multiple Choice
Evaluate the given expression.
21. Combinatorics and Probability
Combinatorics
Multiple Choice
Evaluate the given expression.
A
330
B
120
C
5,040
D
7,920
Verified step by step guidance1
Understand that the expression 11C7 represents a combination, which is used to find the number of ways to choose 7 items from a set of 11 items without regard to order.
Recall the formula for combinations: \( nCk = \frac{n!}{k!(n-k)!} \), where \( n \) is the total number of items, \( k \) is the number of items to choose, and \( ! \) denotes factorial.
Substitute the values into the formula: \( 11C7 = \frac{11!}{7!(11-7)!} \). This simplifies to \( \frac{11!}{7!4!} \).
Calculate the factorials: \( 11! = 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \), \( 7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \), and \( 4! = 4 \times 3 \times 2 \times 1 \).
Simplify the expression by canceling out common terms in the numerator and denominator, and perform the division to find the number of combinations.
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