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The number of arrangements of 10 different things taken 4 at a time in which one particular thing always occurs is
- a)2015
- b)2016
- c)2014
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The number of arrangements of 10 different things taken 4 at a time in...
Here, if 1 thing always occur then we will fix that place. Now 3 places are remaining and 9 things are remaining.
For, rest 3 places total selections of things are (93)(93)and total arrangements of 4 things is 4!4!..
Answer = (9/3)∗4!=84∗24=2016(9/3)∗4!=84∗24=2016
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The number of arrangements of 10 different things taken 4 at a time in...
Given: 10 different things taken 4 at a time, one particular thing always occurs.
To find: Number of arrangements
Solution:
We can fix the one particular thing in one of the four positions and then select the other 3 things from the remaining 9 things.
Number of ways of selecting 3 things from 9 things = 9C3 = (9*8*7)/(3*2*1) = 84
Therefore, the total number of arrangements = 4 * 84 (since we can fix the one particular thing in any of the four positions) = 336
Hence, the correct option is (B) 2016.
To find: Number of arrangements
Solution:
We can fix the one particular thing in one of the four positions and then select the other 3 things from the remaining 9 things.
Number of ways of selecting 3 things from 9 things = 9C3 = (9*8*7)/(3*2*1) = 84
Therefore, the total number of arrangements = 4 * 84 (since we can fix the one particular thing in any of the four positions) = 336
Hence, the correct option is (B) 2016.
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The number of arrangements of 10 different things taken 4 at a time in which one particular thing always occurs isa)2015b)2016c)2014d)none of theseCorrect answer is option 'B'. Can you explain this answer?
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