1)In how many different ways can you roll doubles in a monopoly game when you use two die
2)caterer offers a choice of five desserts from a list of eight for the dessert bar at the prom. How many different groups of desserts could be served?
1.
Sample space = 6*6 = 36
Number of successes (doubles)
= |{11,22,33,44,55,66}|
=6
Figure out the probability for doubles.
2. 8 choose 5
=C(8,5)
where
C(n,r) is defined as the combination of r items chosen from n.
=n!/(r!(n-r)!)
1) To find out the number of different ways to roll doubles in a monopoly game when using two dice, we need to consider the possible outcomes of each die individually.
When rolling one die, there are 6 possible outcomes (1, 2, 3, 4, 5, or 6). For each outcome on the first die, there is only one corresponding outcome on the second die that would result in rolling doubles.
So, for each outcome on the first die, there is one way to roll doubles. Since there are 6 possible outcomes for the first die, there are also 6 different ways to roll doubles.
Hence, in a monopoly game, you can roll doubles in 6 different ways.
2) To determine the number of different groups of desserts that could be served from a choice of five desserts out of eight options, we can use combinations.
In this case, we want to select a group of 5 desserts out of the available 8 options. The order in which we select the desserts does not matter.
The formula to calculate the number of combinations is given by:
nCr = n! / (r!(n-r)!),
where n is the total number of options, and r is the number of options we need to select.
Using this formula, with n = 8 and r = 5, we can calculate the number of different groups of desserts that could be served as follows:
8! / (5!(8-5)!) = 8! / (5!3!) = (8 x 7 x 6) / (3 x 2 x 1) = 56
Therefore, there are 56 different groups of desserts that could be served from the available options.