Question1) Ten students have appeared for a test in which the top five will get unique prizes. fiow many possibie ways are there to get the prize winners?
Studdy Solution
STEP 1
What is this asking? How many different groups of five students can get prizes out of a group of ten? Watch out! The order in which the students are chosen matters, since the prizes are unique!
STEP 2
1. Calculate the number of ways to choose the first prize winner.
2. Calculate the number of ways to choose the second prize winner.
3. Continue calculating for the remaining prize winners.
4. Multiply the possibilities together.
STEP 3
We have **10** students, and *any* of them could win the first prize.
So, there are **10** possibilities for the first prize winner.
Exciting!
STEP 4
Once the first prize is awarded, there are only **9** students left to choose from for the second prize.
This means there are **9** possibilities for the second prize winner.
STEP 5
For the third prize, there are **8** remaining students, so there are **8** possibilities.
For the fourth prize, there are **7** remaining students, so there are **7** possibilities.
And for the fifth prize, there are **6** remaining students, so there are **6** possibilities!
STEP 6
To get the *total* number of ways to award the prizes, we **multiply** the number of possibilities for each prize together.
This is because each choice is independent of the others.
Think of it like a branching tree of possibilities!
STEP 7
So, the total number of ways is .
STEP 8
Let's calculate that: , , , and .
That's a lot of ways to win!
STEP 9
There are **30,240** possible ways to award the prizes.
Was this helpful?
