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Question

The names of 11 fifth-graders, including the top math and the top spelling student in the fifth-grade class, are placed in a hat and randomly selected to sit on the stage with the governor for his visit to the school.
 
Four students are randomly selected to join the governor.
 

Part 1 out of 3
 
a. In how many ways can four students be selected for first chair, second chair, third chair, and fourth chair to join the governor for this occasion?
 
The students can be selected for first chair, second chair, third chair, and fourth chair to join the governor in
ways.

Answer 1

So whenever we are given some total amount and asked to choose only a select few we use the n choose m formula. Which is:

w = (n!)/(m!(n-m)!)

where w is the number of ways we can combine the students n is the total number of students and m is the number we can choose. The ! is the factorial symbol, 4! = 4x3x2x1. so for this problem n = 11, m = 4

w = (11!)/(4!7!)=(11x10x9x8)/(4x3x2x1)= 330

therefore there are 330 ways the students can be selected