Six discrete mathematics student:Bahirah,Dinesh,Johan,Adam,Felina and Syahirah are going to stand in a line. How many ways can they stand if:

Question

a)Syahirah must be in the third position?
b)Dinesh must be second and Fellina third?
c)Boys and girls alternate, with boy starting the line?
d)The first three positions are boysand the last three are girls?
e)Adam can't be on eitherend of the line?

Answer 1

Number of arrangements of n persons in n positions is n!.
Example, 3 people, 3 places, there are 3!=6 possible arrangements.

a) If Syahirah mush be in the third position, there are 5 people left for 5 places. Use the formula above.

b)If Dinesh must be second, and Felina third, there are only 4 people left for 4 positions. Use the formula above.

c) If boys and girls alternate, with boy starting the line (assuming the line is directed, i.e. there is head and tail of the line), then boys are in the 1st, 3rd and 5th position, and girls in the remaining positions.
There are 3 places for 3 boys, and 3 places for 3 girls.
Multiply the number of arrangements for boys, and that of girls to get the answers. Multiplication because the arrangement of boys is (assumed to be) independent of that of girls.

d) Same idea as c) above, figure it out.

e) If Adam is at the beginning of the line, there are 5 positions left for 5 people. Same if he is at the end.
Calculate the number of arrangements for 6 people in six positions, then subtract the number of arrangements that Adam is at the head and tail of the line.

Answer 2

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Answer 3

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