Question

If a bag has $3$ alike mangoes, $4$ alike apples and $2$ alike oranges, then the correct option(s) is/are?

• 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)

Total number of ways of selecting atleast $1$ fruit is $59$

Number of selections of atleast one mango from $3$ alike mangoes $=3$
Number of selections of atleast one apple from $4$ alike apples $=4$
Number of selections of atleast one orange from $2$ alike oranges $=2$
$\therefore$ The number of ways of selecting atleast $1$ of each kind of fruit
$=3\times 4\times 2=24$

Now, the total number of ways of selecting atleast $1$ fruit
$=(3+1)(4+1)(2+1)-1=59$