In how many different ways could the birds be arranged?

[NEHA]

There were three little red birds, two blue birds, and five green birds sitting next to each other on a park bench. In how many different ways could the birds be arranged?

I did:
2R 2B 5G
rrbbggggg

it can be
2*2*5 = 20 ways
or
2+2+5 = 9
9! = 362880 ways

What do you think?

 

[Mrspi]

Re: which way';

there were three little red birds , two blue birds, and five green birds sitting next to each other on a park bench. in how many different ways could the birds be arranged?
i did
2R 2B 5G
rrbbggggg

it can be
2*2*5 = 20 ways
or
2+2+5 = 9
9! = 362880ways what do you think

Here's what I think.

You have 10 different birds to arrange. You can do that in 10! ways....

however, you have 3 red birds (all indistinguishable, I'd think), 2 blue birds, and 5 green birds. There are 3! ways to arrange the red birds, 2! ways to arrange the blue birds, and 5! ways to arrange the green birds.

So, the number of ways to arrange all ten of the birds is

10!
----------
3!*2!*5!

 

[NEHA]

THANK YOU
so
10! = 3628800
3!*2!*5! = 1440
3628800/1440 = 2520 ways