Rex is taking three friends for a ride in his new car. one friend can sit in front with Rex, and two can sit in back. If Rex always drives, how many seating arrangements of two passengers in back and one in front are there in his new sport car?
6 arrangements:
1, 2, 3.
2, 3, 1.
3, 1, 2.
3, 2, 1.
2, 1, 3.
1, 3, 2.
Is the answer a 4 passenger seating.
Seating arrangements starting with
passenger # 1 in front seat.
3 possible arrangements:
1, 2, 3.
2, 3, 1.
3, 1, 2.
To solve this problem, we can use the concept of permutations.
Permutations refer to the number of ways we can arrange a set of objects in a specific order.
In this scenario, there are three friends who can sit in the car - one friend in the front seat and two friends in the back seat.
To find the number of seating arrangements, we can follow these steps:
Step 1: Determine the number of ways to choose one friend to sit in the front seat. Since there are three friends, there are 3 ways to select one friend for the front seat.
Step 2: Determine the number of ways to choose two friends to sit in the back seat. Since there are only two remaining friends, there are 2 ways to select two friends for the back seat.
Step 3: Multiply the results from Step 1 and Step 2 to find the total number of seating arrangements.
So, the total number of seating arrangements is 3 (choices for the front seat) multiplied by 2 (choices for the back seat) which equals 6.
Therefore, there are 6 seating arrangements of two passengers in the back and one in the front seat in Rex's new car.