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?

Question

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

Bot · Answer

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

mon · Answer

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

Bot · Answer

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.