Question

in how many ways 5 red 4 blue 1 green balls be arranged in a row

Answer 1

Hi there!
Here's the answer

Total no. of balls =10

No . of arrangements of these balls = 10!

No. of red balls = 5

No. of arrangements =5!

No. of  blue  balls = 4

No. of arrangements = 4 !

No. of  green  balls = 1

No. of arrangements = 1 !

Total no. of  Arrangements 
= 10! / (5! × 4! × 1!) 
=  27720  ways

:)
Hope it helps

Answer 2

The total no. of ways for arranging 5 red 4 blue 1 green balls  in a row is 1260.  

Step-by-step explanation:

Given:

5 red 4 blue 1 green balls.

Now total balls = $5+4+1$ = $10$

For 'n' objects, with 'a₁' of one kind, 'a₂' of another kind, 'a₃' of another kind and so on, the different arrangements is given as:

$\frac{n!}{a_1!\times a_2!\times a_3!\times.....a_n!}$

Here, $n=10,a_1=5,a_2=4,a_3=1$

So total number of ways for arranging balls = $\frac{10!}{5!\times4!\times1!}$

$=\frac{10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{5\times4\times3\times2\times4\times3\times2\times1}$

Cancel out same digits then the remaining part will be:

$=\frac{10\times9\times8\times7\times6}{4\times3\times2}$

=$\frac{30240}{24}$

=$1260$

Therefore, the total number of arranging the different balls in a row is 1260.