SOLUTION: A student planning her curriculum for the upcoming year must select one of six business courses, one of two mathematics courses, two of seven elective courses, and either one of th

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Question 1148275: A student planning her curriculum for the upcoming year must select one of six business courses, one of two mathematics courses, two of seven elective courses, and either one of three history courses or one of two social science courses. How many different curricula are available for her consideration?
Found 2 solutions by greenestamps, josmiceli:
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


(1) business: 1 of 6 --> "6 choose 1" = 6C1
(2) mathematics: 1 of 2 --> "2 choose 1" = 2C1
(3) electives: 2 of 7 --> "7 choose 2" = 7C2
(4) other: 1 of 3 OR 1 of 2 --> "3 choose 1 plus 2 choose 1" = 3C1+2C1
Note this is equivalent to "5 choose 1" = 5C1

The total number of sets of courses is the product of all those numbers of choices.

C%286%2C1%29%2AC%282%2C1%29%2AC%287%2C2%29%2AC%285%2C1%29

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Use combination formula
C( n, r ) = n! / ( ( n-r)! * r! )
C( 6,1 ) = 6
C( 2,1 ) = 2
----------------------------
C( 7,2 ) = +7%21+%2F+%28+5%21%2A2%21+%29+
C( 7,2 ) = +6%2A7+%2F+2+
C( 7,2 ) = 21
----------------------------
C( 3,1 ) = 3
C( 2,1 ) = 2
---------------------------
+6%2A2%2A21%2A3+%2B+6%2A2%2A21%2A2+
+6%2A2%2A21%2A%28+3+%2B+2+%29+
+756+%2B+504+=+1260+
There are 1,260 different curricula
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Note that the last 2 choices get added because
of the OR.
Get 2nd opinion if needed