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Question

How do you tell if a word problem is a permutation or combination ?


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Solution

Defining permutation or combination:

Permutation is all about the arrangements of objects/elements, whereas combination is about the selection of objects/elements. In permutation, order of elements/objects matters, whereas in the combination order of elements/objects does not matter.

Example 1: How many different teams of 6 students can be chosen from 11 students.

Therefore, Total number of teams of 6 students =C611 Crn=n!(n-r)!r!

=11!11-6!6!=11×10×9×8×7×6!5!6!=11×10×9×8×75×4×3×2×1=262

Example 2: In how many different ways 6 students can be seated in 10 places.

Therefore, Total ways of seating arrangement of 6 students in 10 places =P610 Prn=n!(n-r)!

=10!10-6!=10×9×8×7×6×5×4!4!=151200

Hence, by above conditions we can tell if a word problem is a permutation or combination .


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