Permutations Help (1 Viewer)

[juampabonilla]

1)In Morse code, letters are formed by a sequence of dashes and dots. How many different
letters is it possible to represent if a maximum of ten symbols are used?

2) Five backpackers arrive in a city where there are five youth hostels.
(a) How many different accommodation arrangements are there if there are no restrictions
on where the backpackers stay?
(b) How many different accommodation arrangements are there if each backpacker stays
at a different youth hostel?
(c) Suppose that two of the backpackers are brother and sister and wish to stay in the
same youth hostel. How many different accommodation arrangements are there if the
other three can go to any of the other youth hostels?

 

[braintic]

1)In Morse code, letters are formed by a sequence of dashes and dots. How many different
letters is it possible to represent if a maximum of ten symbols are used?

1 symbol: 2 possibilities
2 symbols: 2^2 = 4 possibilities
3 symbols: 2^3 = 8 possibilities
.
.
.
10 symbols: 2^10 = 1024 possibilities

Summing the GP: 2047 possibilities

 

[braintic]

2) Five backpackers arrive in a city where there are five youth hostels.
(a) How many different accommodation arrangements are there if there are no restrictions
on where the backpackers stay?
(b) How many different accommodation arrangements are there if each backpacker stays
at a different youth hostel?
(c) Suppose that two of the backpackers are brother and sister and wish to stay in the
same youth hostel. How many different accommodation arrangements are there if the
other three can go to any of the other youth hostels?

(a) 5^5

(b) 5!

(c) 5 choices for the brother and sister, times 4^3 choices for the others