# A bag has 4 chocolate, 7 lollipops, and 5 gumballs. If you select 5 randomly, what is the probability that you select all the same type?

Relevance

All lollipops:

(7/16) * (6/15) * (5/14) * (4/13) * (3/12) =>

(7/16) * (2/5) * (5/14) * (4/13) * (1/4) =>

(7/14) * (2/16) * (5/5) * (4/4) * (1/13) =>

(1/2) * (1/8) * 1 * 1 * (1/13) =>

1/208

All gumballs:

(5/16) * (4/15) * (3/14) * (2/13) * (1/12) =>

(5 * 12 * 2) / (16 * 15 * 14 * 13 * 12) =>

(5 * 2) / (16 * 15 * 14 * 13) =>

1 / (8 * 3 * 14 * 13) =>

1 / (104 * 3 * 2 * 7) =>

1 / (208 * 21)

We can't pull 5 chocolates.  Add the probabilities together.

1/208 + 1/(208 * 21) =>

21 / (21 * 208) + 1 / (208 * 21) =>

(21 + 1) / (21 * 208) =>

22 / (21 * 208) =>

11 / (21 * 104) =>

11 / 2184

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• I've got it. We can do 7C5+5C5 (lollipops and gumballs respectively while ignoring chocolate bars as that can't be done). Over the total which is 16C5.

22/4368

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• Total objects = 4 + 7 + 5 = 16

Ratios:

Chocolate --> 4/16 = 25% (0.25) ---> 1.25 if selected randomly 5 times

Lollipops --> 7/16 = 44% (0.4375)---> 2.20 if selected randomly 5 times

Gumballs --> 5/16 = 31% (0.3125)---> 1.56 if selected randomly 5 times

-Cannot recall for second part of the question, sorry.

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