A student must choose 3 books to read from a reading list of 6 distinct books. How many di… — GMAT

A student must choose $3$ books to read from a reading list of $6$ distinct books. How many different combinations of $3$ books can the student select?

A
$15$
B
$18$
$20$ Answer
D
$60$
E
$120$

Answer

The student can select

20

different combinations of

3

books.

To find the number of ways to select

3

books from

6

distinct books when order does not matter, use the combination formula

\binom{n}{k} = \frac{n!}{k!(n-k)!}

. Evaluating

\binom{6}{3} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20

. Thus,

20

is the correct number of combinations.

Step-by-Step Solution

Identify the counting method

Since the order in which the books are selected does not matter, use the combinations formula

\binom{n}{k} = \frac{n!}{k!(n-k)!}

Selection of a group without regard to order requires combinations.

Substitute the given values into the formula

Here

n = 6

and

k = 3

, so

\binom{6}{3} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1}

Apply

n=6

available items and

k=3

chosen items.

Simplify the expression

\frac{120}{6} = 20.

Perform the basic arithmetic division.

Key Concept

Combinations and Group Selections

Estimated Time:45s

Question

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Step-by-Step Solution

Key Concept

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