question archive In a gymnastics club, 10 gymnasts practice forming a human pyramid
In a gymnastics club, 10 gymnasts practice forming a human pyramid
Subject:MathPrice:2.86 Bought7
In a gymnastics club, 10 gymnasts practice forming a human pyramid. The pyramid uses only 6 gymnasts at any one time. There are 3 gymnasts in the bottom row, 2 in the second row, and 1 at the top.
If any gymnast can fill any position in the pyramid, how many different arrangements of gymnasts are there?
Nine runners have made it to the zone cross-country running finals. Harriett is considered the favourite to win based on her previous times. If she does win, in how many different orders can the other racers finish?
A local hockey club is setting up an online system for registration for its players.
Seven-character passwords will be assigned to each player and each password will start with the letter S to indicate the home club's team name, Sharks. The other digits in the password are made up of the numbers 4 through 9, and no digit can be repeated. How many passwords can the hockey club create?
Purchase A New Answer
Custom new solution created by our subject matter experts
GET A QUOTE
Answer Preview
1) 151200 arrangements
2)40320 different orders
3) 720 passwords
Step-by-step explanation
1)
The top of the pyramid can be any of 10
Left middle can be any of 9 (one already top)
Right middle can be any of 8 (one top and one left middle)
Left bottom can be any of 7
Middle bottom can be any of 6
Right bottom can be any of 5
Thus, there are 10*9*8*7*6*5 or 151200 arrangements.
2) Since there are 9 runners and one runner (Harriett) is considered to win the race, there are 8*7*6*5*4*3*2*1 or 8! ways to determine orders where the other racers finish.
Thus, there are 40320 different orders for the other racers to finish the race
3) There are 7 characters in a password. The first character is the letter S. Thus, there are 6 characters left.
Also, the other digits in the password are made up of the numbers 4 through 9, and no digit can be repeated.
Since there are 6 numbers from 4 to 9, there are 6*5*4*3*2*1 password combinations.
Therefore, the hockey club can create 720 passwords.
