Download App

Permutations — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsPermutations3 Marks
Question
In how many ways can $4$ prizes be distributed among $5$ students, when
  1. No student gets more than one prize?
  2. A student may get any number of prizes?
  3. No student gets all the prizes?
✓

Answer

  1. $4$ prizes be distributed among $5$ students so that no student gets more than one prize can be done in
$^5\text{p}_4= \frac{5!}{(5-4)!}=\frac{5!}{(1)!}= 5! \ \text{ways}.$
  1. The first prize can be given away in $5$ ways as it may be given to anyone of the $5$ students. The second prize can also be given away in $5$ ways, since if may be obtained by the student who has already received a prize. Similarly, third and fourth prize can be given away in $5$ ways.
Hence, the number of ways in which all the prize can be given away $= 5 \times 5 \times 5 \times 5 = 625$
  1. Since any of the $5$ students may get all the prizes. So, the number of ways in which a student gets all the $4$ prizes is $5.$
So, the number of ways in which a student does not get all the prizes $= 625 - 5 = 620$

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 "3 Marks Question" from Permutations→Permutations — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Find the number of words with or without meaning which can be made using all the letters of the word AGAIN. If these words are written as in a dictionary, what will be the $50^{th}$ word?
→
Evaluate the following limits: $\lim _{x \rightarrow 0} \frac{2 x}{\sqrt{a+x}-\sqrt{a-x}}$.
→
Find the sum of n terms of the geometric progression $1, -a, a^2, -a^3 ... n$ terms $($if a $\ne -1).$
→
The sum of two numbers is 6 times their geometric means, show that the numbers are in the ratio $(3+2\sqrt{2}):\big(3-2\sqrt{2}\big).$
→
Write the component statements of the following compound statements and check whether the compound statement is true or false.
24 is a multiple of 4 and 6.
→
Evaluate the following limits:
$\lim\limits_{\text{x}\rightarrow\infty}\frac{3\text{x}^{-1}+4\text{x}^{-2}}{5\text{x}^{-1}+6\text{x}^{-2}}$
→
In how many ways can a football team of $11$ players be selected from $16$ players? How many of them will.
  1. Include $2$ particular players?
  2. Exclude $2$ particular players?
→
Find the point in yz-plane which is equidistant from the points A(3, 2, -1), B(1, -1, 0) and C(2, 1, 2).
→
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated.
→
The vertices of the triangle are $A(5, 4, 6), B(1, -1, 3)$ and $C(4, 3, 2)$.The intenal bisector of angle $A$ meets $BC$ at $ D.$ Find the coordinates of $D$ and the length $AD.$
→