An English class consists of twenty students, and five are to be chosen to give speeches in a school competition. In how many different ways can the teacher choose the team, given the following conditions? (a) The order of the speakers is important. 7296 Incorrect: Your answer is incorrect. (b) The order of the speakers is not important.
Answer)
When order is not important we use combinations
Ncr = n!/(r!*(n-r)!)
Where n! = n*n-1*n-2*n-3*n-4*n-5*....till 1
For example
5! = 5*4! = 5*4*3! = 5*4*3*2! = 5*4*3*2*1
When order is important we use permutations
Npr = n!(n-r)!
A)
Order is important
N = 20
R = 5
20p5 = 20!/(20-5)! = 20!/15! = 1860480
B)
Order is not important
20c5 = 20!/(5!*15!) = 15504
An English class consists of twenty students, and five are to be chosen to give speeches...