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If 7Pr = 210, what is the value of r?
- a)3
- b)4
- c)5
- d)6
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If7Pr= 210, what is the value of r?a)3b)4c)5d)6Correct answer is optio...
Understanding the Problem
To find the value of r in the equation 7Pr = 210, we need to apply the formula for permutations. The formula for permutations is given by:
nPr = n! / (n - r)!
In this case, n = 7, so we can rewrite the equation as:
7Pr = 7! / (7 - r)!
Breaking Down the Equation
Now, substituting into the equation we have:
7! / (7 - r)! = 210
Calculating 7!:
- 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040
Thus, we can rewrite the equation as:
5040 / (7 - r)! = 210
Isolating (7 - r)!
To isolate (7 - r)!, we multiply both sides by (7 - r)!:
5040 = 210 × (7 - r)!
Now, we can divide both sides by 210:
(7 - r)! = 5040 / 210
Calculating the right side:
- 5040 / 210 = 24
So, we have:
(7 - r)! = 24
Finding the Value of (7 - r)
Now, we need to find which factorial equals 24:
- 4! = 4 × 3 × 2 × 1 = 24
Thus, we have:
7 - r = 4
Solving for r
Now, solving for r:
7 - 4 = r
Therefore, r = 3.
Conclusion
The value of r is 3, which corresponds to option 'A'.
To find the value of r in the equation 7Pr = 210, we need to apply the formula for permutations. The formula for permutations is given by:
nPr = n! / (n - r)!
In this case, n = 7, so we can rewrite the equation as:
7Pr = 7! / (7 - r)!
Breaking Down the Equation
Now, substituting into the equation we have:
7! / (7 - r)! = 210
Calculating 7!:
- 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040
Thus, we can rewrite the equation as:
5040 / (7 - r)! = 210
Isolating (7 - r)!
To isolate (7 - r)!, we multiply both sides by (7 - r)!:
5040 = 210 × (7 - r)!
Now, we can divide both sides by 210:
(7 - r)! = 5040 / 210
Calculating the right side:
- 5040 / 210 = 24
So, we have:
(7 - r)! = 24
Finding the Value of (7 - r)
Now, we need to find which factorial equals 24:
- 4! = 4 × 3 × 2 × 1 = 24
Thus, we have:
7 - r = 4
Solving for r
Now, solving for r:
7 - 4 = r
Therefore, r = 3.
Conclusion
The value of r is 3, which corresponds to option 'A'.
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Community Answer
If7Pr= 210, what is the value of r?a)3b)4c)5d)6Correct answer is optio...
7Pr = 7P3
r = 3
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Question Description
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