Question

From $3$ cocoa nuts, $4$ apples, and $2$ oranges, how many selections of fruit can be made, a taking at least one of each kind?

Answer 1

Given that there are $3$ cocoa nuts , $4$ apples and $2$ oranges

Now we have to make selection of fruits by taking at least one of the each kind.

Total number of ways cocoa nuts can be selected is $2^3-{{}^{3}C}_0=8-1=7$

Total number of ways apples can be selected is $2^4-{{}^{4}C}_0=16-1=15$

Total number of ways oranges can be selected is $2^2-{{}^{2}C}_0=4-1=3$

Therefore total number of selections of fruit can be made by taking at least one of each kind is $7\times 15\times 3=315$