Question

Question 7 Find r if

(i) 5Pr = 2^6 P(r-1)

(ii) 5Pr = 6P(r-1).

Class X1 - Maths -Permutations and Combinations Page 148

Answer 1

(1) ⁵Pr = 2{⁶P(r-1)}
5!/r! = 2 × 6!/(r -1)! {use the formula, ⁿPᵥ = n!/(n-v)! }
5!/(5 -r)! = 2 × 6 × 5!/(6 -r +1 )!
1/(5 -r)! = 12/(7-r )(6 - r )(5 - r)!
1 = 12/(7 - r)( 6 -r)
42 - 13r + r² = 12
r² - 13r + 30 = 0
(r -10)(r - 3) = 0
r = 10, 3 but we will take only 0 ≤ r ≤ 5
so, r = 3


(ii) ⁵Pr = {⁶P(r-1)}
5!/(5 - r)! = 6 × 5!/(6 - r +1)!
1 = 6/(7-r)( 6 - r)
42 - 13r + r² = 6
r² -13r + 36 = 0
r² -9r - 4r + 36 = 0
(r - 9)(r - 4) = 0
r = 9, 4 but we will take only 0≤ r ≤ 5
so, r = 4

Answer 2

Answer:

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