What is the formula for combinations

1 answer:

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Note: , where nPr is the formula for permutations of n objects taken r at a time.Example:How many different committees of 4 students can be chosen from a group of 15?Answer:There are possible combinations of 4 students from a set of 15.There are 1365 different committees

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Carol has 1 5/8 cups of yogurt to make smoothies. Each smoothie uses 1/3 cup of yogurt. What is the maximum number of smoothies

nikdorinn [45]

Answer: The answer is 4.

Step-by-step explanation: Given that -

The number of cups of yogurt that Carol has to make smoothies is given by

$c_y=1\dfrac{5}{8}=\dfrac{13}{8},$

and the number of cups of yogurt that each smoothies uses is given by

$c_s=\dfrac{1}{3}.$

Let 'n' be the number of smoothies that Carol can make with the available yogurt, then we have

$n\times c_s\leq c_y\\\\\\\Rightarrow n\times \dfrac{1}{3}\leq \dfrac{13}{8}\\\\\\\Rightarrow n\leq\dfrac{39}{8}\\\\\\\Rightarrow n\leq 4\dfrac{7}{8}\\\\\\\Rightarrow n=4.$