A man bought two vanilla ice cream cones, three chocolate cones, four strawberry cones and one pistachio cone for his ten children. In how many ways can he distribute the flavors among the children?
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Well, the P can go 10 ways
The V can go then 9*8 ways
the C can go then 7*6*5
and the S can go 4*3*2*1
so ways: 10!
check my thinking.
but what if we did the strawberry first?
the S can go 10*9*8*7 ways
the V can go 6*5
the P can go 4 ways
the C can go 3*2*1
again, 10!
Believe me?
Yes I did 10!/3!4!2!
number of ways of n! of which we have a of one kind, b of another kind , c of another kind ...
= n!/(a!b!c!..)
so you would have 10!/(2!3!4!) = 12600
that's what I got:) Thanks
To find the number of ways the man can distribute the ice cream cones among his children, we can use the concept of permutations and combinations.
Since the order in which the children receive their cones doesn't matter, we need to find the number of combinations (not permutations) in this case.
Let's consider the number of ways the vanilla cones can be distributed to the children. Since there are 2 vanilla cones and 10 children, we need to select 2 children to receive the vanilla cones. This can be done in 10 choose 2 ways, which is denoted as C(10,2).
C(10,2) = 10! / (2! * (10-2)!) = 45
Similarly, we can calculate the number of ways for the other flavors:
- Chocolate cones: C(10,3) = 10! / (3! * (10-3)!) = 120
- Strawberry cones: C(10,4) = 10! / (4! * (10-4)!) = 210
- Pistachio cones: C(10,1) = 10! / (1! * (10-1)!) = 10
To find the total number of ways to distribute all the cones among the children, we need to multiply the number of ways for each flavor:
Total ways = Number of ways for vanilla cones * Number of ways for chocolate cones * Number of ways for strawberry cones * Number of ways for pistachio cones
Total ways = 45 * 120 * 210 * 10 = 11,340,000
Therefore, there are 11,340,000 ways the man can distribute the flavors among his ten children.