Answer

Verified

430.5k+ views

**Hint:**we are given a problem in which they have to distribute different prizes to the different candidates so there are different ways to distribute the prizes. In this, we have to distribute the prize in order so when the order does matter then we will use permutation.

**Formula used:**

The number of permutations of n objects taken r at a time is determined by the following formula:

$P(n,r) = \dfrac{{n!}}{{\left( {n - r} \right)!}}$

Here $n$= total no of different elements

$r$ = arrangement pattern of the elements

Both $r$ and $n$ are positive integers

**Complete step by step answer:**

Step1: We are given first, second and third prizes to be distributed among $5$people and one person should not get two prizes. Hence here we have to distribute the prizes in an order

Hence we will use permutations because here order matters

Step2: We will use the formula of permutation

$P(n,r) = \dfrac{{n!}}{{\left( {n - r} \right)!}}$

Here $n = 5$ and $r = 3$

Step3: Substituting the value of n and r in the formula we will get the number of permutation

$\Rightarrow {}^5{P_3} = \dfrac{{5!}}{{\left( {5 - 3} \right)!}}$

On expanding the expressions we get

$\Rightarrow {}^5{P_3} = \dfrac{{5 \times 4 \times 3 \times 2 \times 1}}{{2 \times 1}}$

On dividing the numerator by$2$we get:

$\Rightarrow {}^5{P_3} = 5 \times 4 \times 3$

$\Rightarrow {}^5{P_3} = 60$

**Hence, the number of ways in which the three prizes can be distributed $ = 60$ ways.**

**Note:**

In such types of problems students mainly get confused whether to apply the formula of permutation or of combination. So they have to understand the difference between permutation and combination when order doesn’t matter it is combination and when order matters it is the permutation

We can also solve it simply:

The first prize can be given in $5$ ways. Then the second prize can be given in $4$ ways and the third prize in $3$ ways

(Since a competitor cannot get two prizes) and hence the no. of ways $ = 5 \times 4 \times 3$

$ = 60$ ways

Keep in mind that

$P(n,r) = \dfrac{{n!}}{{\left( {n - r} \right)!}}$

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Which are the Top 10 Largest Countries of the World?

Difference Between Plant Cell and Animal Cell

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE