*** = my answers
Jason wants to choose 9 players for his track team. There are 12 players to choose from. How many different teams can Jason make?
A: 21
B: 112
C: 200***
D: 306
How many different ways can the students at a school elect the president, vice president, and secretary from a group of 5 people?
A: 120
B: 60***
C: 20
D: 15
There are 20 entries in the chess tournament. How many ways can the entries finish in first, second, and third place?
A: 340
B: 6,840***
C: 7,220
D: 8,350
An ice cream shop offers the following toppings:
- chocolate chips
- strawberry sprinkles
- caramel
- hot fudge
- whipped cream
- gummy bears
If a sundae must have exactly four toppings, how many different sundaes can you make?
A: 15***
B: 24
C: 12
D: 18
Could someone check my answers please?
#1. 12C9 = 12C3 = 220
200 is close, but I suspect a typo
#2. ok
#3. ok
#4. ok
can we gettbfhj3jh some freal reas help pdslsdlsll
there are 20 entries i the chess tournament how many ways can the entries finish in first second and third place
The number of ways the 20 entries can finish in first, second, and third place is given by:
20P3 = 20 x 19 x 18 = 6,840
Therefore, the answer is B) 6,840.
whats the answer to the question with jason
The number of different teams Jason can make by choosing 9 players out of 12 is:
12C9 = 220
Therefore, the answer is A) 220.
what about the one after ?
The number of different sundaes that can be made with exactly four toppings from a list of six toppings is:
6C4 = 15
Therefore, the answer is A) 15.
Sure! Let's go through the answers and explanations to check if they are correct.
Question 1: Jason wants to choose 9 players for his track team. There are 12 players to choose from. How many different teams can Jason make?
To find the number of different teams Jason can make, we need to calculate the combination of 12 players choose 9 players. The formula for combinations is nCr = n! / (r! * (n-r)!), where n is the total number of options and r is the number of options chosen.
Plugging in the values, we get 12! / (9! * (12-9)!). Simplifying this, we have 12! / (9! * 3!). The factorial cancels out, giving us (12 * 11 * 10) / (3 * 2 * 1) = 1,320 / 6 = 220.
Therefore, the correct answer is not listed among the options provided. None of the options are correct, so D is the correct answer.
Question 2: How many different ways can the students at a school elect the president, vice president, and secretary from a group of 5 people?
To find the number of different ways to elect the three positions from a group of 5 people, we need to calculate the permutation of 5 people taken 3 at a time. The formula for permutations is nPr = n! / (n-r)!, where n is the total number of options and r is the number of options chosen.
Plugging in the values, we get 5! / (5-3)! = 5! / 2! = (5 * 4 * 3) / (2 * 1) = 60.
Therefore, the correct answer is B: 60.
Question 3: There are 20 entries in the chess tournament. How many ways can the entries finish in first, second, and third place?
To find the number of different ways the entries can finish in first, second, and third place, we need to calculate the permutation of 20 entries taken 3 at a time. Using the permutation formula, we get 20! / (20-3)! = 20! / 17!.
Simplifying this expression, we have (20 * 19 * 18 * 17!) / 17!. The 17! terms cancel out, giving us (20 * 19 * 18) = 6,840.
Therefore, the correct answer is B: 6,840.
Question 4: An ice cream shop offers six toppings: chocolate chips, strawberry sprinkles, caramel, hot fudge, whipped cream, and gummy bears. If a sundae must have exactly four toppings, how many different sundaes can you make?
To calculate the number of different sundaes with four toppings, we need to find the combination of six toppings choose four toppings. Using the combination formula, we get 6! / (4! * (6-4)!).
Simplifying this expression, we have 6! / (4! * 2!). The factorials cancel out, giving us (6 * 5) / (2 * 1) = 30 / 2 = 15.
Therefore, the correct answer is A: 15.
Based on these explanations, your answers are correct for Questions 2 and 4. However, your answer for Question 1 is incorrect, and the correct answer is not listed among the options provided. Your answer for Question 3 is correct as well.