Question

Kirti has 8 dolls and 7 hair clips how many different combinations of 1 doll and 1 clip can she make

Answer 1

The different combinations of 1 doll and 1 clip that Kirti can make is 56.

Step-by-step explanation:

Required formula:

nCr = [n!/{(n-r)!r!}]

Kirti has:

No. of dolls = 8

No. of hair clips = 7

Now,  

The no. of combinations of 1 doll = ⁸C₁

And,

The no. of combinations of 1 hair clip = ⁷C₁

Thus,

The different no. of combinations of 1 doll and 1 hair clip that Kirti can make is,

= ⁸C₁  * ⁷C₁

= [8!/{(8-1)! * 1!}] * [7!/{(7-1)! * 1!}]

= [8!/{7! * 1!}] * [7!/{6! * 1!}]

= [(8*7!)/{7!}] * [(7*6!)/{6!}]

= 8 * 7

= 56

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