# A bag contains 9 red, 8 orange, and 7 green jellybeans

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Qn18. A bag contains 9 red, 8 orange, and 7 green jellybeans.  What is the probability of reaching into the bag and randomly withdrawing 16 jellybeans such that the number of red ones is 5, the number of orange ones is 7, and the number of green ones is 4?  Express your answer as a fraction or a decimal number rounded to four decimal places.

Qn19.

Larissa is ordering apple pie at a restaurant, and the server tells her that she can have up to four toppings: walnuts, pecans, whipped cream, and caramel. Since she cannot decide how many of the toppings she wants, she tells the server to surprise her. If the server randomly chooses which toppings to add, what is the probability that Larissa gets just walnuts and pecans? Express your answer as a fraction or a decimal number rounded to four decimal places.

The first question can be answered using combination method, note that that total number of jellybeans in the bag are,

9+8+7 = 24

The number of ways of withdrawing 16 out of 24 is 24C16 = 735471

The number of ways of selecting 5 red rellybeans is 9C5 = 126

The number of ways of selecting 7 orange from 8 is 8C7 = 8

The number of ways of selecting 7 out of 4 is 7C4 = 35

Note that you can use the COMBIN() function in excel to calculate the combination values.

The possible outcomes are 126+8+35 = 169

The probability is 169/735471 = 0.0002

Thus, the answer to question 18 is 0.0002

Let us know if you have similar probability questions.