Question

lara has a bag with tiles numbered 1 through 7 in it. in how many orders can she pull 4 tiles out of the bag?

Explanation:

Step1: Identify the problem type

This is a permutation problem where we want to find the number of ways to arrange 4 tiles out of 7, where order matters. The formula for permutations is \( P(n, r)=\frac{n!}{(n - r)!} \), where \( n = 7 \) (total number of tiles) and \( r = 4 \) (number of tiles to be pulled out).

Step2: Calculate the factorial values

First, calculate \( n! = 7! = 7\times6\times5\times4\times3\times2\times1 = 5040 \) and \( (n - r)!=(7 - 4)!=3!=3\times2\times1 = 6 \).

Step3: Apply the permutation formula

Substitute the values into the formula: \( P(7, 4)=\frac{7!}{(7 - 4)!}=\frac{5040}{6} \).

Step4: Perform the division

\( \frac{5040}{6}=840 \).

Answer:

840