Find n if ^ n - 1 P_3 :^n P_4 = 1:9 - Vidyadip

Question

Find n if $^{n - 1}{P_3}{:^n}{P_4} = 1:9$

✓

Answer

Here $^{n - 1}{P_3}{:^n}{P_4} = 1:9$
$\therefore \frac{{(n - 1)!}}{{(n - 4)!}}:\frac{{n!}}{{(n - 4)!}} = 1:9$.
$ \Rightarrow \frac{{(n - 1)!}}{{(n - 4)!}} \times \frac{{(n - 4)!}}{{n!}} = \frac{1}{9}$
$ \Rightarrow \frac{{(n - 1)!}}{{n!}} = \frac{1}{9} \Rightarrow \frac{{(n - 1)!}}{{n(n - 1)!}} = \frac{1}{9}$
$ \Rightarrow \frac{1}{n} = \frac{1}{9} \Rightarrow n = 9$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 1 marks)" from PERMUTATIONS AND COMBINATIONS→PERMUTATIONS AND COMBINATIONS — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Show that the set of letters needed to spell "CATARACT" and the set of letters needed to spell "TRACT" are equal?

Write an equation representing a pair of lines through the point (a, b) and parallel to the coordinate axes.

Find the derivative of $x^{-3} (5 + 3x)$

Find the radian measure corresponding to the following degree measures: 135°

Evaluate $\lim _\limits{x \rightarrow 0} \frac{\sin 4 x}{\sin 2 x}$

Two dice are thrown. The events A, B and C are as follows:
A: getting an even number on the first die
B: getting on odd number on the first die
C: getting the sum of the numbers on the dice $\le 5$
Describe the event A'

Write the maximum and minimum values of $\sin(\sin\text{x}).$

If $3\tan(\text{x}-15^{\circ})=\tan(\text{x}+15^{\circ}),0<\text{x}<90^{\circ},$ find x.

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that repetition of the digits is allowed

If $\frac{3+5+7+\ ...\ +\text{Upto n terms}}{5+8+11+\ ...\ \text{Upto 10 terms}}=7,$ then find the value of n.