Need help with this problem

[rachey21]

Probability question- need help!!

10 students are running for the offices of president, vice president, secretary and treasurer. Of the 10 students, two of them are identical twins who like to switch places form time to time. However, their names appear separately on the ballot. If this is the case, what is the probability that at Tia, one of the twins, can spend at least some time as president?


I know that there are 10C4 ways that 10 students can be president, vice president, secretary and treasurer.

 

[tkhunny]

Okay, now do the rest.

Pick Tia as president and calculate the number of ways to do that.
Pick Tia-Twin as president and calculate the number of ways to do that.

Try to relax. If you need an instant answer, you may wish to consider paying for it. We have only volunteers who wander by as they are able.

 

[soroban]

Hello, rachey21!

Ten students are running for the offices of President, Vice President, Secretary and Treasurer.
Of the ten students, two of them are identical twins who like to switch places form time to time.
However, their names appear separately on the ballot.
If this is the case, what is the probability that at Tia, one of the twins,
can spend at least some time as president?

I know that there are 10C4 ways that 10 students can be President, V.P., Secretary and Treasurer.
. . No!

There are: \(\displaystyle _{10}P_4 = 5,040\) ways that the offices can be filled.


After working out the answer the long way, I saw an "eyeball" approach.

Tia can spend some time being President
. . if either Tia or her twin is elected President.

And that probability is: .\(\displaystyle \dfrac{2}{10} \,=\,\dfrac{1}{5}\)