Annual Mathlympics 2009

4 men and 4 women are to be seated at a round table for dinner. If the men and women take alternate seats, how many arrangements are possible?


4 x 3 x 2 x 1 x 4 x 3 x 2 x 1 = 576 ways


The arrangement for men is 4 x 3 x 2 x 1 and the arrangement for women is also 4 x 3 x 2 x 1.

Annual Mathlympics 2009

Janice was given a set of 5 different coloured beads to make a bracelet.If she has to use all of the 5 beads, how many different ways can Janice make the bracelet?


5 x 4 x 3 x 2 x 1 / 2 = 60 ways


There are 5 ways to pick the first bead, 4 ways to pick the second bead, 3 ways to pick the third bead, 2 ways to pick the fourth bead and 1 way to pick the last bead. As the bracelet can be turn over, the arrangement ABCDE is the same as EDCBA. So the number of ways is halved.