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