A research team needs to select a subcommittee of 3 scientists from a department containin… — GMAT

A research team needs to select a subcommittee of 3 scientists from a department containing 7 scientists. How many different 3-member subcommittees can be selected?

Cevap: 35 subcommittees

Cevap

35 different subcommittees can be selected.

The total number of ways to choose a committee of 3 members from a group of 7 without regard to order is given by the combination formula

C(7,3) = \frac{7 \times 6 \times 5}{3 \times 2 \times 1} = 35

Adım Adım Çözüm

Determine whether the selection depends on order.

Order does not matter since all 3 members of the subcommittee have equal roles.

When order does not matter in group selection, combinations (

nCr

) must be used rather than permutations (

nPr

Apply the combination formula

C(n,k) = \frac{n!}{k!(n-k)!}

with

n=7

and

k=3

C(7,3) = \frac{7 \times 6 \times 5}{3 \times 2 \times 1}

This counts the unique groups of 3 that can be chosen from a pool of 7.

Calculate the numerical result.

Dividing

7 \times 6 \times 5 = 210

3 \times 2 \times 1 = 6

yields 35.

Anahtar Kavram

Combinations and Group Selections

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