Permutations Question (1 Viewer)

[mikey1312]

1. In how many ways can a boat crew of eight women be arranged if three of the women can only row on the bow side and two others can only row on the stroke side?
2. In Morse code, letters are formed by a sequence of dashes and dots. How many different letters it it possible to represent if a maximum of ten symbols are used?
Please show working so I can understand.
Thanks.

 

[Nooblet94]

1. First we place the 3 women. Assuming there's 4 seats on each side that means that there's 4P3 ways to place them. Now we consider the other two; there's 4P2 ways to place them. Now there's 3 people left and 3 places to seat them, so 3!. Number of ways = 4P3*4P2*3!

2. There's two different symbols we can use, a dash or a dot. If we use one symbol we have 2 ways of doing it, two symbols=2^2, three=2^3 etc. So the answer is 2+2^2+2^3...2^10