Question

In a certain community, there are $3$ families consisting of a single parent and $1$ child, $3$ families consisting of a single parent and $2$ children, $5$ families consisting of $2$ parents and a single child, $7$ families consisting of $2$ parents and $2$ children, and $6$ families consisting of $2$ parents and $3$ children. If a parent and child from the same family are to be chosen, how many possible choices are there?

Short answer

The possible no. of choices are$83$.

Step-by-step solution

Step 1. Given information.

It is given that,

No. of families consisting of a single parent and $1$child localid="1649220666180" $=3$

No. of families consisting of a single parent and $2$children $=3$

No. of families consisting of $2$ parents and a single child$=5$

No. of families consisting of $2$ parents and $2$children$=7$

No. of families consisting of $2$ parents and $3$ children$=6$

Step 2. Find the possible no. of choices.

No. of ways of selecting a parent and child from $3$ families consisting

of a single parent and $1$ childrole="math" localid="1649221212323" $=3\times 1\times 1=3$

No. of ways of selecting a parent and child from $3$ families consisting of a single parent and $2$ children$=3\times 1\times 2=6$

No. of ways of selecting a parent and child from $5$ families consisting of $2$ parents and a single child$=5\times 2\times 1=10$

No. of ways of selecting a parent and child from $7$ families consisting of $2$ parents and $2$ children$=7\times 2\times 2=28$

No. of ways of selecting a parent and child from $6$families consisting of $2$parents and $3$children$=6\times 2\times 3=36$

Therefore, the no. of possible choices are$3+6+10+28+36=83$.