a)Out of 16 children, 7 are under 3 years old If 2 children under 3 years old and 3 children 3 or more years old are allowed on climbing equipment. How many combinations of 5 children are possible? (1764)
b)Allan is 2 years old and his friend Hannah is 4 years old. If restrictions in part(b) apply, how many combinations of 5 children are possible which include both Allan and Hannah?(168)
The answers are in the bracket
Thanks
Of a group of 16 children at a preschool, for safety reasons, only 5 are allowed on the climbing equipment at one time?
2020-08-08 2:18 pm
回答 (2)
2020-08-08 3:05 pm
✔ 最佳答案
a)U represents a child under 3 years old. n(U) = 7
U' represents a child 3 or more years old. n(U') = 16 - 7 = 9
To form a possible combination, select 2U from 7U (₇C₂), and select 3U from 9U(₉C₃).
The number of possible combinations
= ₇C₂ × ₉C₃
= 21 × 84
= 1764
====
b)
Firstly, selected both Allan and Hannah (₂C₂), and 6U and 8U' are left.
Then, select one more U from 6U left (₆C₁), and select 2 more U' from 8U' left (₈C₂).
Number of combinations
= ₂C₂ × ₆C₁ × ₈C₂
= 1 × 6 × 28
= 168
2020-08-08 2:34 pm
What's "7 are under 3 years old If 2 children under 3 years old " ?
收錄日期: 2021-04-18 18:35:56
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