Download App

Permutations — MATHS STD 11 Science — Question

Gujarat 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 × 5 × 5 × 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 "(Each question 3 marks)" from Permutations→Permutations — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Find the rational number having the following decimal expansions:$0.\overline{3}$
→
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow{\frac{\pi}{4}}}\frac{1-\tan\text{x}}{1-\sqrt{2}\sin\text{x}}$
→
Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas: $y^2 - 4y - 3x + 1 = 0$.
→
Differentiate the following function with respect to x:$(\text{x}\sin\text{x}+\cos\text{x})(\text{e}^\text{x}+\text{x}^2\log\text{x})$
→
For any two sets, prove that:
$\text{A}\cup(\text{A}\cap\text{B})=\text{A}.$
→
Find the ratio in which the line joining (2, 4, 5) and (3, 5, 4) is divided by the yz-plane.
→
Find the point of intersection of the following pairs of lines: bx + ay = ab and ax + by = ab.
→
Evaluate the following:$\sum_\limits{\text{n}=1}^{11}(2+3^\text{n})$
→
If P and Q are two sets such that P has 40 elements, $\text{P}\cup\text{Q}$ has 60 elements and $\text{P}\cap\text{Q}$ has 10 elements, how many elements does Q have?
→
Let A = {x : x $\in$ N}, B = {x : x = 2n, n $\in$ N}, C = {x : x = 2n - 1, n $\in$ N} and D = {x : x is a prime natural number}. Find: $\text{C}\cap\text{D}$
→