Question

If ⁵⁶P_{r + 6} : ⁵⁴P_{r + 3} = 30800 : 1, then the value of r is ______.

Options

• 41

• 14

• 10

• 51

Answer 1

If ⁵⁶P_{r + 6} : ⁵⁴P_{r + 3} = 30800 : 1, then the value of r is 41.

Explanation:

`(56!)/((50 - r)!) = 30800((54!)/((51 - r)!))`

`\implies` 56 × 55 = `30800/(51 - r)`

`\implies` 51 – r = `30800/(56 xx 55)`

`\implies` 51 – r = 10

`\implies` 41 = r