Question

The kindergarten teacher has $25$ kids in her class. She takes $5$ of them at a time, to zoological garden as often as she can, without taking the same $5$ kids more than once. Then the number of visits, the teacher makes to the garden exceeds that of a kid by

• A. ${}^{25}{C}_5-{}^{24}{C}_4$
• B. ${}^{24}{C}_5$
• C. ${}^{25}{C}_5-{}^{24}{C}_5$
• D. ${}^{24}{C}_4$

Answer 1

Answer: (A), (B)

${}^{24}{C}_5$

Number of visits teacher makes $={}^{25}{C}_5$
Number of visit by a kid $={}^{24}{C}_4$
Difference between the number of trips made by teacher and a kid $={}^{25}{C}_5-{}^{24}{C}_4={}^{24}{C}_5$
$(\because {}^n{C}_r+{}^n{C}_{r+1}={}^{n+1}{C}_{r+1})$