Question

Find the number of different choices that can be made from $3$ apples, $4$ bananas and $5$ mangoes, if at least one fruit is to be chosen?

• A. $60$
• B. $120$
• C. $119$
• D. $59$

Answer 1

Answer: (C)

$119$

$3$ Apples $⟶$ $A$

$9$ Bananas $⟶$ $B$

$5$ Mangoes $⟶$ $C$

${\left(A\right)}^3{\left(B\right)}^4{\left(C\right)}^5{a}^p{b}^q{c}^r$

Number of ways of selecting $(p+1)(q+1)(r+1)-1$

$=(3+1)(4+1)(5+1)=4\times 5\times 6-1=120-1=119$

Therefore number of ways$=119$