SOLUTION: A boy has three 10-cent coins and five 5-cent coins in his pocket. The boy draws four coins for good luck. Calculate the probability of the event that the coins drawn will be enoug

Question 1198728: A boy has three 10-cent coins and five 5-cent coins in his pocket. The boy draws four coins for good luck. Calculate the probability of the event that the coins drawn will be enough to pay 30 cents for the purchase.
Answer by ikleyn(52880) (Show Source): You can put this solution on YOUR website!
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A boy has three 10-cent coins and five 5-cent coins in his pocket.
The boy draws four coins for good luck. Calculate the probability
of the event that the coins drawn will be enough to pay 30 cents for the purchase.
~~~~~~~~~~~~~~~~~~~

Favorable outcomes are THESE:

    10-cent    5-cent     Total          Total
     coins     coins      coins          cents
  ----------------------------------------------------

       3         1       3+1 = 4    3*10+5 = 35 > 30
       2         2       2+2 = 4    2*10 + 2*5  = 30


There is no other favorable combination for the given conditions.


So, the number of all favorable outcomes is 2.


The number of all possible outcomes is the number of all possible quadruples of 3+5 = 8 coins,

i.e.   =  = 70.


So, the probability under the problem's question is

    P =  =  = .    ANSWER

Solved and carefully/thoroughly explained.

In this problem, the order/(ordering) of coins does not matter, so we use COMBINATIONS.

-----------------

On Combinations, see introductory lessons
    - Introduction to Combinations
    - PROOF of the formula on the number of Combinations
    - Problems on Combinations
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Combinatorics: Combinations and permutations".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.

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