If 16Pr-1 : 15Pr-1 = 16 : 7 then find r.
Answers
Concept
A permutation is an arrangement of several items taken one at a time or all at once in a specific order. Take the following ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. These 10 numbers can be used to create 5040 unique 4-digit PINs in total. P(10,4) = 5040. This is a basic illustration of a permutation.
It is simple to calculate the permutations using: ⁿPr = n!/(n-r)!
Given
¹⁶Pr₋1 : ¹⁵Pr₋1 = 16÷7
Find
while solving the above expression we need to get the value of r.
Solution
¹⁶Pr₋1 : ¹⁵Pr₋1 = 16÷7 is in the form of ⁿPr .
hence we apply the formula.
¹⁶Pr₋1 : ¹⁵Pr₋1 = 16!/[16₋(r₋1)]! : 15!/[15₋(r₋1)]!
16!/[16₋(r₋1)]! ÷ 15!/[15₋(r₋1)]! = 16 ÷ 7
16!/(17₋r)! ÷ 15!/(16₋r)! = 16 ÷ 7
16!/(17₋r)! × (16₋r)!/15! = 16/7
16×15!/(17₋r)(16₋r)! × (16₋r)!/15! = 16/7
after cancelling the terms we get,
16/(17₋r) = 16/7
16×7 = 16(17₋r)
112 = 272 ₋ 16r
112 ₋ 272 = ₋16r
₋160 = ₋16r
r = 160/6
r = 10
hence we get the value of r as 10.
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Answer:
The value of r is 10.
Explanation:
A permutation is an arrangement of several items taken one at a time or all at once in a specific order.
It is simple to calculate the permutations using the formula: ⁿPr = n!/(n-r)!
We are given that ¹⁶Pr₋1 : ¹⁵Pr₋1 = 16÷7
We need to calculate r.
Using formula, we get
¹⁶Pr₋1 : ¹⁵Pr₋1 = 16!/[16₋(r₋1)]! : 15!/[15₋(r₋1)]!
16!/[16₋(r₋1)]! ÷ 15!/[15₋(r₋1)]! = 16 ÷ 7
16!/(17₋r)! ÷ 15!/(16₋r)! = 16 ÷ 7
16!/(17₋r)! × (16₋r)!/15! = 16/7
16×15!/(17₋r)(16₋r)! × (16₋r)!/15! = 16/7
16/(17₋r) = 16/7
16×7 = 16(17₋r)
112 = 272 ₋ 16r
112 ₋ 272 = ₋16r
₋160 = ₋16r
r = 160/6
r = 10
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