Permutations & Combinations
Permutation and Combination
star_batch_jee_advanced_2025
Grade None
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:
25C5 - 24C4
24C5
25C5 - 24C5
24C4
Step-by-Step Solution
Key Concept: The excess visits by the teacher over any individual kid equals the combinations that include that specific kid, which can be expressed in two equivalent forms.
The total number of visits the teacher makes equals the total number of ways to select 5 kids from 25, which is $^{25}C_5$. For any specific kid, the number of visits that kid makes equals the number of ways to select 4 more kids from the remaining 24, which is $^{24}C_4$. The difference is $^{25}C_5 - ^{24}C_4$. We can verify this equals $^{24}C_5$ by using the identity: $^{25}C_5 = ^{24}C_5 + ^{24}C_4$, which gives $^{25}C_5 - ^{24}C_4 = ^{24}C_5$.
Correct Answer: 1,2