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alexgriva [62]
2 years ago
7

On a camping trip you bring 12 items for 4 dinners. For each dinner you use 3 items. In how many ways can you choose items for t

he first dinner? for the second? for the third? for the fourth?
​
Mathematics
1 answer:
Rashid [163]2 years ago
6 0

Answer:

  • 220 options, 84 options, 20 options, 1 option

Step-by-step explanation:

<h3>The first dinner</h3>

Combinations of 3 out of 12 items

  • 12C3 = 12!/(12-3)!3! = 12!/9!3! = 12*11*10/2*3 = 220
<h3>The second dinner</h3>

Combinations 3 out of remaining 9 items

  • 9C3 = 9!/(9 - 3)!3! = 9!/6!3! = 9*8*7/2*3 = 84
<h3>The third dinner</h3>

Combinations of 3 out of remaining 6 items

  • 6C3 = 6!/(6 - 3)!3! = 6!/3!3! = 6*5*4/2*3 = 20
<h3>The fourth dinner</h3>

Combinations of 3 out of 3 remaining items

  • 3C3 = 3!/(3 - 3)!3! = 3!/0!3! = 1
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