# Coin tossing problem.

• Sep 22nd 2011, 10:50 PM
nasir31971
Coin tossing problem.
Q.Four coins are tossed simatanously, in how many distinct ways these coins can show up??

I think it is going to be 16..
Do u guys agree with me???
• Sep 23rd 2011, 01:15 AM
CaptainBlack
Re: Coin tossing problem.
Quote:

Originally Posted by nasir31971
Q.Four coins are tossed simatanously, in how many distinct ways these coins can show up??

I think it is going to be 16..
Do u guys agree with me???

Are they indistinguishable?

If they are distinguishable then there are 2^4 ways they can fall, if indistinguishable there are 4 ways the can fall.

CB
• Sep 23rd 2011, 01:16 AM
matheagle
Re: Coin tossing problem.
assuming you mean heads and tails
it is $2^4$
• Sep 23rd 2011, 04:08 AM
nasir31971
Re: Coin tossing problem.
Thanks.....i also go with 2^4
• Sep 23rd 2011, 08:39 AM
Soroban
Re: Coin tossing problem.
Hello, nasir31971!

Quote:

Four coins are tossed simultanously.
In how many distinct ways these coins can show up?

I think it is going to be 16.
Do u guys agree with me?

CaptainBlack raised a legitimate point.

If the four coins are distinct -- say, a penny, nickel, dime, and a quarter --
. . then there are: . $2^4 = 16$ outcomes.

If the four coins are identical, we may be counting the Heads and Tails only.
In this case, there are only 5 outcomes:
. . 3 Heads, 1 Tail
. . 2 Heads, 2 Tails
. . 1 Head, 3 Tails
. . All Tails

• Sep 23rd 2011, 09:38 AM
CaptainBlack
Re: Coin tossing problem.
Quote:

Originally Posted by nasir31971
Thanks.....i also go with 2^4

While there is some ambiguity in the wording I think the clause that says they were tossed simultaneously implies that they are indistinguishable and so the answer is 4.

Note the outcomes in this case are not equally likely (while in the other case they are)

CB