Answer

Verified

329.7k+ views

**Hint:**From the given data it is clear that the first row consists of 6 girls so these 6 girls can be arranged in $6!$ possible ways. And in the second row there are 20 boys with the corner spots fixed for the tallest boys of the class so they can be arranged for $2!$ ways and the remaining 18 boys can be arranged in $18!$ ways. So, the total ways in which the students can be arranged will be the product of these values.

**Complete step-by-step solution:**

In this question, we are given that a class photograph is to be taken with the front row consisting of 6 girls and 20 boys standing behind them and the corner two positions are reserved for the two tallest boys of the class. We need to find out how many ways these students can be arranged.

So, according to the given data it is clear that the first row consists of 6 girls.

So, let us find ways for the first row of girls to be arranged.

$ \Rightarrow $Number of ways for 6 girls $ = 6!$

Now, the second row consists of 20 boys standing but the corner spots are fixed for the two tallest boys of the class.

$ \Rightarrow $Number of these 2 boys can be arranged$ = 2!$

So, the remaining 18 boys will be arranged in

$ \Rightarrow $Number of ways for 18 boys $ = 18!$

So, the total number of ways all these students can be arranged is given by

$ \Rightarrow $Total number of possible arrangements $ = 6! \times 2! \times 18! = 18! \times 1440$

**Hence, the students can be arranged for $18! \times 1440$ ways.**

**Note:**Here, note that

$ \Rightarrow n! = n \times \left( {n - 1} \right) \times \left( {n - 2} \right) \times ...... \times 1$

So, therefore, 18! Will be equal to

$ \Rightarrow 18! = 18 \times 17 \times 16 \times ...... \times 1$

Here for arrangement we could also use the formula of permutations as ${}^nP_r = \dfrac{n!}{{n-r}!}$ but sometimes students are confused b/w permutation and combination so for solving these types of problems we should know all the formulae.

Recently Updated Pages

Assertion The resistivity of a semiconductor increases class 13 physics CBSE

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

How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE

Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE

What are the possible quantum number for the last outermost class 11 chemistry CBSE

Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

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

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

Write two gases which are soluble in water class 11 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Fill the blanks with proper collective nouns 1 A of class 10 english CBSE

What organs are located on the left side of your body class 11 biology CBSE

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