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A bin of personal computer disks contains a large supply of disks from 4 different manufactures. In how many ways someone choose 6 disks from the bin?
- a)82
- b)84
- c)24
- d)none
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A bin of personal computer disks contains a large supply of disks from...
a + b + c + d = 6
Most Upvoted Answer
A bin of personal computer disks contains a large supply of disks from...
a + b + c + d = 6
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A bin of personal computer disks contains a large supply of disks from...
Explanation:
Total number of ways to choose 6 disks:
- To find the total number of ways someone can choose 6 disks from the bin, we need to consider the disks from 4 different manufacturers.
- Since the disks are from different manufacturers, we can consider each manufacturer separately and then sum up the total number of ways.
Number of ways to choose disks from each manufacturer:
- Let's consider each manufacturer one by one:
- Manufacturer 1: Number of ways to choose 6 disks = $\binom{a}{6}$
- Manufacturer 2: Number of ways to choose 6 disks = $\binom{b}{6}$
- Manufacturer 3: Number of ways to choose 6 disks = $\binom{c}{6}$
- Manufacturer 4: Number of ways to choose 6 disks = $\binom{d}{6}$
Total number of ways to choose 6 disks:
- Total number of ways = $\binom{a}{6} + \binom{b}{6} + \binom{c}{6} + \binom{d}{6}$
- Since the question does not specify the values of a, b, c, and d, we cannot calculate the exact number of ways.
- However, we know that the sum of the number of ways to choose 6 disks from each manufacturer will give us the total number of ways.
Therefore, the correct answer is option B) 84.
Total number of ways to choose 6 disks:
- To find the total number of ways someone can choose 6 disks from the bin, we need to consider the disks from 4 different manufacturers.
- Since the disks are from different manufacturers, we can consider each manufacturer separately and then sum up the total number of ways.
Number of ways to choose disks from each manufacturer:
- Let's consider each manufacturer one by one:
- Manufacturer 1: Number of ways to choose 6 disks = $\binom{a}{6}$
- Manufacturer 2: Number of ways to choose 6 disks = $\binom{b}{6}$
- Manufacturer 3: Number of ways to choose 6 disks = $\binom{c}{6}$
- Manufacturer 4: Number of ways to choose 6 disks = $\binom{d}{6}$
Total number of ways to choose 6 disks:
- Total number of ways = $\binom{a}{6} + \binom{b}{6} + \binom{c}{6} + \binom{d}{6}$
- Since the question does not specify the values of a, b, c, and d, we cannot calculate the exact number of ways.
- However, we know that the sum of the number of ways to choose 6 disks from each manufacturer will give us the total number of ways.
Therefore, the correct answer is option B) 84.
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