SOLUTION: in aclassroom club there are 22 girls and 28 boys . the class is to elect to apresident and a treasurer. what is the number of ways for choosing these candidatess
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Question 1154704: in aclassroom club there are 22 girls and 28 boys . the class is to elect to apresident and a treasurer. what is the number of ways for choosing these candidatess
You can put this solution on YOUR website! For each pair that is possible, call it
a and b, you can have:
[ a is pres. ] and [ b is tres. ]
[ b is pres. ] and [ a is tres. ]
so, order does matter and you will use
permutations and not combinations
whether someone is a girl or a boy
does not matter
P( n ,r ) = n! / ( n - r )!
P( n, r ) = 50! / 48!
2,450 different ways
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feel free to get a 2nd opinion
In all, there are 22 + 28 = 50 students and 2 different positions.
Anyone of students can be selected for the first position, giving 50 options.
Anyone of remaining 49 students can be selected for the second position, giving 49 options.
The total number of ways is 50*49 = 2450. ANSWER
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Notice, that in this problem the goal is NOT to select a pair, without looking on the order in the pair.
The goal is to select persons to certain positions, which makes the order essential.
