Geo777
31.03.2020 •
Mathematics
I have 12 friends I would like to invite to dinner but can only accommodate ten. How many ways can I invite ten if: a. There are no restrictions. Simplify your answer to one final number. For b and c Do not simplify your answers. Leave in combinatorics form. b. Two of my friends are married so if I invite one, I have to invite the other. c. Two of my friends do not like each other so if invite one, I cannot invite the other.
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Ответ:
there are 66 ways to invite 10 if there are no restrictions
Step-by-step explanation:
a. to get it we use the combination rule
C(n,r)=?
(n,r)=(nr)=n!/(r!(n−r)!)=
C(n,r)=C(12,10)
=12!/(10!(12−10)!) = 12!/(10!2!)
= 12x11x10x9x8x7x6x5x4x3x2x1/(10x9x8x7x6x5x4x3x2x1(2x1)
= 79833600/(604800x2)
= 79833600/1209600 = 66
Ответ:
so answer is D