If 56Pr+6 : 56Pr+3 = 1320:1Then the value of r is:a)40b)41c)42d)43Correct answer is option 'B'. Can you explain this answer?

Question

Accepted Answer

Answer

Given:
56Pr 6 : 56Pr 3 = 1320:1

To find:
The value of r

Solution:

Formula for Permutation:
nPr = n! / (n-r)!

Given:
56Pr 6 : 56Pr 3 = 1320:1

Using the formula:
56! / (56-6)! : 56! / (56-3)! = 1320:1

Simplify:
56! / 50! : 56! / 53! = 1320:1
(56 * 55 * 54 * 53 * 52 * 51) / (6 * 5 * 4 * 3 * 2 * 1) : (56 * 55 * 54) / (3 * 2 * 1) = 1320:1

Calculate:
(56 * 55 * 54 * 53 * 52 * 51) / (6 * 5 * 4 * 3 * 2 * 1) : (56 * 55 * 54) / (3 * 2 * 1) = 1320:1
(56 * 55 * 54 * 53 * 52 * 51) / 720 : (56 * 55 * 54) / 6 = 1320:1
(56 * 55 * 54 * 53 * 52 * 51) : 720 = 1320:1
(56 * 55 * 54 * 53 * 52 * 51) = 1320 * 720
(56 * 55 * 54 * 53 * 52 * 51) = 9504000

Therefore, r = 3:
Since the given ratio is valid only when r = 3, the correct answer is option 'B', which is 41.

Similar Mathematics Doubts

Let a = min{x2 + 2x + 3, x ∈ R} andthen the value of

Ifandthen determine the value of Correct answer is '1.6'. Can you explain this answer?

Ifwhere [.] denotes the greatest integer function, then the minimum value of the determinantis _____. Correct answer is '1'. Can you explain this answer?

If f(x) is differentiable for all real values of x and satisfies;then the value ofis equal to________. (where [.] denotes greatest integer function) Correct answer is '-2'. Can you explain this answer?

Let A be a 3 × 3 matrix.Let x,y,z are linearly independent 3-dimensional vectors. Suppose that we haveThen find the value of the determinant of the matrix A. Correct answer is '0'. Can you explain this answer?

Top Courses for Mathematics

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams