SOLUTION: jarred has 7 hamsters. how many diffrent ways can he choose 3 of them to take with him to show and tell? a. 343 b. 210 c. 21 d. 35

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Question 89825: jarred has 7 hamsters. how many diffrent ways can he choose 3 of them to take with him to show and tell?
a. 343
b. 210
c. 21
d. 35
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since order doesn't matter, we can use the combination formula:





n%21%2F%28n-r%29%21r%21 Start with the given formula



7%21%2F%287-3%29%213%21 Plug in n=7 and r=3



7%21%2F4%213%21 Subtract 7-3 to get 4


Expand 7!
%287%2A6%2A5%2A4%2A3%2A2%2A1%29%2F4%213%21


Expand 4!
%287%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%284%2A3%2A2%2A1%293%21



%287%2A6%2A5%2Across%284%2A3%2A2%2A1%29%29%2F%28cross%284%2A3%2A2%2A1%29%293%21 Cancel



%287%2A6%2A5%29%2F3%21 Simplify


Expand 3!
%287%2A6%2A5%29%2F%283%2A2%2A1%29



210%2F%283%2A2%2A1%29 Multiply 7*6*5 to get 210



210%2F6 Multiply 3*2*1 to get 6



35 Now divide



So 7 choose 3 (where order doesn't matter) yields 35 unique combinations


So the answer is d)