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Find the number of arrangements of 5 things taken out of 12 things, in which one particular thing must always be included.
- a)39,000
- b)37,600
- c)39,600
- d)36,000
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Find the number of arrangements of 5 things taken out of 12 things, in...
Given: 12 things and we have to select 5 things such that one particular thing must always be included.
To find: Number of arrangements of 5 things taken out of 12 things.
Solution:
Let's consider the given particular thing as one of the 5 selected things. Then we have to select 4 more things from the remaining 11 things.
Number of ways of selecting 4 things out of 11 things = 11C4
Number of arrangements of 5 things taken out of 12 things, in which one particular thing must always be included = 11C4 × 4!
[Because once we select the 5 things, we can arrange them in 5! ways.]
Now, let's simplify the expression for 11C4:
11C4 = (11 × 10 × 9 × 8) / (4 × 3 × 2 × 1) = 330
Therefore, the number of arrangements of 5 things taken out of 12 things, in which one particular thing must always be included = 330 × 4! = 39,600
Hence, the correct option is (c) 39,600.
To find: Number of arrangements of 5 things taken out of 12 things.
Solution:
Let's consider the given particular thing as one of the 5 selected things. Then we have to select 4 more things from the remaining 11 things.
Number of ways of selecting 4 things out of 11 things = 11C4
Number of arrangements of 5 things taken out of 12 things, in which one particular thing must always be included = 11C4 × 4!
[Because once we select the 5 things, we can arrange them in 5! ways.]
Now, let's simplify the expression for 11C4:
11C4 = (11 × 10 × 9 × 8) / (4 × 3 × 2 × 1) = 330
Therefore, the number of arrangements of 5 things taken out of 12 things, in which one particular thing must always be included = 330 × 4! = 39,600
Hence, the correct option is (c) 39,600.
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Community Answer
Find the number of arrangements of 5 things taken out of 12 things, in...
Apply formula - n-1^ C r-1
here n = 12, r = 5, no.of arrangement = 5!
hence,
11C4 × 5! = 39600 (c)
here n = 12, r = 5, no.of arrangement = 5!
hence,
11C4 × 5! = 39600 (c)
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Find the number of arrangements of 5 things taken out of 12 things, in which one particular thing must always be included.a)39,000b)37,600c)39,600d)36,000Correct answer is option 'C'. Can you explain this answer?
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