Question

The kindergarten teacher has 30 kids in her class. She takes 6 of them at a time, to a zoological garden often as she can, without taking the same 6 kids more than once. Then the number of visits, the teacher makes to the garden exceeds that of a kid by

• A. $^{29}C_6$
• B. $^{30}C_6 - ^{29}C_5$
• C. $^{30}C_5$
• D. $^{30}C_6 - ^{29}C_6$

Answer 1

Answer: (B)

${}^{30}C_6 - {}^{29}C_5$

Answer 2

1. Total visits by the teacher: The teacher selects 6 kids from 30, so total visits =

$${}^{30}C_6$$

2. Visits by a given kid: For a fixed kid, she is always present, so the remaining 5 kids are chosen from the other 29. Thus, visits by the kid =

$${}^{29}C_5$$

3. Difference: The excess visits = Total visits − Kid’s visits

$${}^{30}C_6 - {}^{29}C_5$$