Question

In how many ways can six people sit in a six-passenger car?

Answer 1

Hint: In this problem, we have to find, in how many ways can six people sit in a six-passenger car. We know that there are six people and six seats. we can now see that first seat is occupied by a person, who is any of the person out of six passengers, the second seat is occupied by another person who is a choice out of 5 passengers and the third and the remaining seat are filled in this manner, which will give the result as permutation of 6.

Complete step by step solution:
We know that we have to find out how many ways six people can sit in a six-passenger car.
We know that there are six people and six seats.
We can see that for seat no.1, we have choices out of six passengers.
For seat no.2, we have five choices, for seat.no 3 we have four choices, for seat.no 4 we have three choices, for seat.no 5 we have two choices and seat.no 6 has 1 chance.
This can be written as,
\[\Rightarrow 6\times 5\times 4\times 3\times 2\times 1=6!\]
Which is permutation of the number 6.
We can now multiply the above step to get
\[\Rightarrow 6\times 5\times 4\times 3\times 2\times 1=6!=720\]
\[{{\Rightarrow }^{6}}{{P}_{6}}=\dfrac{6!}{\left( 6-6 \right)!}=\dfrac{6!}{1}=720\]
Therefore, 720 ways are there for six people to sit in a six-passenger car.

Note: Students make mistakes while understanding the concepts of permutation, where permutation determines the number of techniques that determines the number of possible arrangements in a set when the order of arrangement matters. We can also use formulas to find the answer.
Permutation, \[_{n}{{P}_{r}}=\dfrac{n!}{\left( n-r \right)!}\]
Where, n = 6, r = 6.
Therefore, 720 ways are there for six people to sit in a six-passenger car.