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The number of permutations of 10 different things taken 4 at a time in which one particular thing never occurs is
- a)3020
- b)3025
- c)3024
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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The number of permutations of 10 different things taken 4 at a time in...
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In this question, we need to find the number of permutations of 10 different things taken 4 at a time in which one particular thing never occurs.
Let us name the particular thing as 'X'.
Total number of permutations of 10 different things taken 4 at a time = ^10P4 = 10 × 9 × 8 × 7 = 5040
We need to subtract the number of permutations in which X occurs.
Number of permutations of 9 different things taken 3 at a time when X is fixed at one position = ^9P3 = 9 × 8 × 7 = 504
We can fix X at any of the 4 positions. Therefore, the number of permutations in which X occurs = 4 × 504 = 2016
Hence, the number of permutations in which X never occurs = Total number of permutations - Number of permutations in which X occurs = 5040 - 2016 = 3024
Therefore, the correct answer is option 'C'.
In this question, we need to find the number of permutations of 10 different things taken 4 at a time in which one particular thing never occurs.
Let us name the particular thing as 'X'.
Total number of permutations of 10 different things taken 4 at a time = ^10P4 = 10 × 9 × 8 × 7 = 5040
We need to subtract the number of permutations in which X occurs.
Number of permutations of 9 different things taken 3 at a time when X is fixed at one position = ^9P3 = 9 × 8 × 7 = 504
We can fix X at any of the 4 positions. Therefore, the number of permutations in which X occurs = 4 × 504 = 2016
Hence, the number of permutations in which X never occurs = Total number of permutations - Number of permutations in which X occurs = 5040 - 2016 = 3024
Therefore, the correct answer is option 'C'.
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The number of permutations of 10 different things taken 4 at a time in...
Out of 10 one thing isn't accepted so the total will be 9 and then by formula : 9P4 =9!/9-4! =9!/5! =362880/120 =your answer is on your calculator
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The number of permutations of 10 different things taken 4 at a time in which one particular thing never occurs isa)3020b)3025c)3024d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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