Question

There are $4$ oranges, $5$ apples and $6$ mangoes in a basket. In how many ways can a person make a selection when select at least one fruit from each kind?

Answer 1

A fruit can be selected from basket in $5\times 6\times 7-1=209$ ways

oranges alone can be selected in $4$ ways

apples alone can be selected in $5$ ways

mangoes alone can be selected in $6$ ways

oranges and apples alone can be selected in $4\times 5=20$ ways

apples and mangoes alone can be selected in $5\times 6=30$ ways

mangoes and oranges alone can be selected in $6\times 4=24$ ways

Required number of ways $=209-4-5-6-20-30-24=120$ ways