There are 40 entries in the science fair. How many ways can the entries finish in first, second, and third place?
A. 240
B. 1,480
C. 12,640
D. 59,280
There are 40 choices for first place, then 39 choices for second place (since one entry has already won first), and 38 choices for third place. So the number of ways they can finish is:
40 x 39 x 38 = 59,280
Therefore, the answer is D.
A bag contains tiles with the letters A-R-I-T-H-M-E-T-I-C. Amelia chooses a tile without looking and doesn’t replace it. She chooses a second tile without looking. What is the probability that she will choose the letter I both times?
A. 1/25
B. 1/45
C. 2/45
D. 2/55
There are 12 tiles in the bag, and the probability of choosing an "I" on the first draw is 1/12. However, since Amelia does not replace the tile, there are only 11 tiles left in the bag for the second draw, and only one "I" remains. Therefore, the probability of choosing an "I" on the second draw given that she chose an "I" on the first draw is 1/11.
To find the probability of both events occurring (choosing an "I" twice in a row), we need to multiply the probabilities together:
(1/12) x (1/11) = 1/132
So the answer is not one of the given options. The closest option is D, which is also incorrect.
There's only 10 letters in arithmetic
You are correct. Since there are 10 letters in "ARITHMETIC", the probability of choosing "I" on the first draw is 1/10, and the probability of choosing "I" on the second draw, given that "I" was chosen on the first draw and not replaced, is 1/9.
Therefore, the probability of choosing "I" twice in a row is:
(1/10) x (1/9) = 1/90
So the answer is not one of the given options, and the closest option is B, which is incorrect.
A sandwich shop offers the following toppings. How many two-topping sandwiches can you make?
Options:
Tomato
Lettuce
Bacon
Cheese
Mustard
Answers:
A. 8
B. 10
C. 12
D. 20
To make a two-topping sandwich, we need to choose two toppings out of the five options. We can use the combination formula:
nCr = n! / r! (n-r)!
where n is the total number of options and r is the number of options we want to choose.
In this case, we have n = 5 (the five toppings) and r = 2 (we want to choose two toppings). Plugging these values into the formula:
5C2 = 5! / 2! (5-2)! = 5! / 2! 3! = (5x4) / (2x1) = 10
So there are 10 different two-topping sandwiches we can make.
Therefore, the answer is B.
A bag contains tiles with the letters C-O-M-B-I-N-A-T-I-O-N-S. Lee chooses a tile without looking and doesn’t replace it he chooses a second file without looking what is the probability that he will choose the letter O both times?
A. 1/132
B. 1/72
C. 1/66
D. 1/23
There are 13 tiles in the bag, and the probability of choosing an "O" on the first draw is 2/13, since there are two "O" tiles out of 13 total tiles. However, since Lee does not replace the tile, there are only 12 tiles left in the bag for the second draw, and only one "O" remains. Therefore, the probability of choosing an "O" on the second draw given that he chose an "O" on the first draw is 1/12.
To find the probability of both events occurring (choosing an "O" twice in a row), we need to multiply the probabilities together:
(2/13) x (1/12) = 1/78
So the answer is not one of the given options. The closest option is A, which is also incorrect.
Am 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