There are 4 oranges, 5 apples, 7 mangoes in a fruit basket. The number of ways of selecting at least one…
There are 4 oranges, 5 apples, 7 mangoes in a fruit basket. The number of ways of selecting at least one fruit from among the fruits in the basket is
$210$
$240$
$209$
$239$
Solution
Considering fruit of same kind to be identical.
Now, if there are $p$ identical things of $1^{\text {st }}$ kind, $q$ identical of $2^{\text {nd }}$ kind and $r$ identical of $3^{\text {rd }}$ kind then total number of ways of selecting any number of objects are
$(\mathrm{p}+1)(\mathrm{q}+1)(\mathrm{r}+1)$
in above given case
Total number of ways $=(4+1)(5+1)(7+1)=240$
But there is one case in which 0 oranges, 0 apples and 0 mangoes are selected
total no. of ways of selecting atleast one fruit $=240-1=239$.