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Zorluk: OrtaCounting Principles

A military supply depot has 66 different types of field rations, 44 different types of hydration packs, and 33 different types of medical kits. A soldier must build a standardized supply bundle containing exactly 22 different types of field rations, 11 hydration pack, and 11 medical kit. How many different supply bundles can be created?

  1. 180Cevap
  2. B
    360
  3. C
    72
  4. D
    22

Cevap

180
To find the total number of distinct supply bundles, we must calculate the number of ways to make each independent selection and multiply them together. First, calculating the number of ways to choose 22 rations from 66 requires combinations because order does not matter: C(6,2)=15C(6, 2) = 15. There are 44 ways to choose a hydration pack and 33 ways to choose a medical kit. Multiplying these together using the Fundamental Counting Principle yields 15×4×3=18015 \times 4 \times 3 = 180 possible bundles.

Adım Adım Çözüm

1
Determine the number of ways to select the field rations.
C(6,2)=6×52×1=15C(6, 2) = \frac{6 \times 5}{2 \times 1} = 15 ways.
Since the order in which the two rations are selected does not matter, we use the combinations formula.
2
Determine the number of ways to select the hydration pack and the medical kit.
44 ways to select a hydration pack and 33 ways to select a medical kit.
Selecting 11 item from a group of nn items gives nn possible choices.
3
Calculate the total number of possible supply bundles.
15×4×3=18015 \times 4 \times 3 = 180 different supply bundles.
Apply the Fundamental Counting Principle by multiplying the number of independent choices together.

Anahtar Kavram

Combinations and the Fundamental Counting Principle
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Konular

Counting Principles

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