Question

Each child of a group gives a gift to other children. Total number of gifts are 110. Find the number of children in a group.

Answer 1

Let there are n number of child.

\(\because\) Each child gives a gift to other children.

\(\therefore\) Total gifts = ⁿP₂.

\(\therefore\)  ⁿP₂ = 110 (\(\because\) Total gifts given  = 110)

⇒ n(n - 1) = 110

⇒ n(n - 1) = 11 x 10 = 11(11 - 10)

\(\therefore\) n = 11

\(\therefore\) Number of children is 11