Question

From a bag of fruits which contains $3$ mangoes, $4$ apples and $2$ oranges, then select the correct option(s)

• A. Total number of ways of selecting atleast $1$ of each kind of fruit is $24$
• B. Total number of ways of selecting atleast $1$ fruit is $60$
• C. Total number of ways of selecting atleast $1$ of each kind of fruits is $23$
• D. Total number of ways of selecting atleast $1$ fruit is $59$

Answer 1

Answer: (A), (D)

The correct options are
A Total number of ways of selecting atleast $1$ of each kind of fruit is $24$
D Total number of ways of selecting atleast $1$ fruit is $59$

Number of selections of atleast one mango from $3$ mangoes $=3$
Number of selections of atleast one apple from $4$ apples $=4$
Number of selections of atleast one orange from $2$ oranges $=2$
$\therefore$ Required number of selections of fruits $=3\times 4\times 2=24$

Now selecting atleast one fruit from $3$ mangoes, $4$ apples and $2$ oranges is
$=(3+1)(4+1)(2+1)-1=59$