Questions: Arrangement of Washers Find the probability that if 7 different-sized washers are arranged in a row, they will be arranged in order of size. Use a TI-83 Plus/TI-84 Plus calculator and round the answer to six decimal places. The probability of the washers arranged by size is .

Solution Steps

To find the probability that 7 different-sized washers are arranged in order of size, we need to consider the total number of possible arrangements and the number of favorable arrangements (where the washers are in order of size).

1. Total Arrangements: The total number of ways to arrange 7 washers is given by the factorial of 7 (7!).
2. Favorable Arrangements: There is only one way to arrange the washers in order of size.
3. Probability Calculation: The probability is the ratio of the number of favorable arrangements to the total number of arrangements.

The total number of ways to arrange 7 different-sized washers is given by the factorial of 7, denoted as \( 7! \). Calculating this, we have: \[ 7! = 5040 \]

There is only one way to arrange the washers in order of size. Thus, the number of favorable arrangements is: \[ \text{Favorable Arrangements} = 1 \]

The probability \( P \) that the washers are arranged in order of size is the ratio of the number of favorable arrangements to the total number of arrangements: \[ P = \frac{\text{Favorable Arrangements}}{\text{Total Arrangements}} = \frac{1}{5040} \approx 0.0001984127 \] Rounding this to six decimal places gives: \[ P \approx 0.000198 \]

Final Answer