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 tile without looking. What is the probability that he will choose the letter O both times?
A. Start Fraction 1 over 132 End Fraction
B. Start Fraction 1 over 72 End Fraction
C. Start Fraction 1 over 66 End Fraction
D. Start Fraction 1 over 23 End Fraction
There are a total of 13 letters in the bag, and only 2 of them are O's. When Lee chooses the first tile, there is a 2/13 chance that he chooses an O. Since he does not replace the tile, there are only 1 O left in the bag for him to choose from out of a total of 12 tiles. Therefore, the probability of choosing an O twice is:
Probability = (2/13) * (1/12) = 1/78
Therefore, the answer is:
D. Start Fraction 1 over 23 End Fraction
A pizza shop offers the toppings shown below. How many different 3-topping pizzas can you make?
pepperoni
mushrooms
sausage
onion
ham
A. 6
B. 10
C. 4
D. 5
To find the number of different 3-topping pizzas you can make, you need to use combinations. The order of the toppings does not matter, so we can use the combination formula:
n C r = n! / (r! * (n-r)!)
where n is the total number of items (toppings) and r is the number of items (toppings) to choose.
In this case, we have n = 5 (since there are 5 toppings) and we want to choose 3 toppings (r = 3). Plugging these values into the formula, we get:
5 C 3 = 5! / (3! * (5-3)!)
= (5 x 4 x 3 x 2 x 1) / ((3 x 2 x 1) x (2 x 1))
= 10
Therefore, there are 10 different 3-topping pizzas that can be made.
The answer is B. 10.
To find the probability that Lee will choose the letter O both times, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Step 1: Total number of possible outcomes
Since Lee chooses a tile without looking and doesn't replace it, the total number of tiles decreases by 1 each time. So, the total number of possible outcomes for the first choice is 12 (since there are 12 letters in the word "COMBINATIONS"). After the first choice, there are only 11 tiles left, so the total number of possible outcomes for the second choice is 11.
Total number of possible outcomes = 12 (for the first choice) * 11 (for the second choice) = 132
Step 2: Number of favorable outcomes
Since we are interested in choosing the letter O both times, we need to find the number of O tiles in the bag. The word "COMBINATIONS" contains 2 occurrences of the letter O.
Number of favorable outcomes = 2 (for the first choice) * 1 (for the second choice) = 2
Step 3: Calculate the probability
The probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 2 / 132
Simplifying the fraction, we get:
Probability = 1 / 66
Therefore, the correct answer is C. (Start Fraction 1 over 66 End Fraction)