A class of 26 students includes 12 who play football 15 who

A class of 26 students includes 12 who play football, 15 who play basketball, and 4 who play both soccer and baseball. How many students in the class play neither piano nor guitar? Show work

A college offers 2 introductory courses in history, 3 in science, 2 in philosophy, 4 in mathematics, and 3 in English. If a freshman takes one course in each area during her first semester, how many course selections are possible? Show work

A couple is planning to have 4 children. They could be all girls, all boys, or some of each. How many groupings are possible? Solve using the multiplication principle of counting. Show work

Solution

(1) number of play football + number of play basketball - number of both

=12+15-4

=23

So answer is 26-23=3 students

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(2) 2*3*2*4*3 = 144

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(3) Let G be girl

Let B be the boy

So the possible groupings are

{GGGG, GBBB, BGBB, BBGB, BBBG

GGBB, GBGB, GBBG, BBGG, GGBB,BGGB

GGGB, GGBG, GBGG, BGGG,

BBBB}

There are 2^4 =16