Problem 39
Question
In how many ways can five children posing for a photograph line up in a row?
Step-by-Step Solution
Verified Answer
There are 120 different ways the five children can line up in a row for a photograph.
1Step 1: Identify problem type
Recognize that this is a permutations problem because the order of the children matters in the arrangement.
2Step 2: Apply permutation formula
The formula for permutations is \( P(n,r) = n! / (n - r)! \) where n is the total number of items, and r is the number of items being arranged. Since all five children are being put in line, r is equivalent to n, which simplifies the formula to \( P(n,n) = n! \)
3Step 3: Substitute into formula
Substitute n = 5 in the formula \( P(n,n) = n! \) which makes it \( P(5,5) = 5! \)
4Step 4: Calculate permutation
Calculate \( 5! \) which equals \( 5 * 4 * 3 * 2 * 1 = 120 \)
Other exercises in this chapter
Problem 38
In Exercises 37-42, use a graphing utility to graph the first 10 terms of the sequence. (Assume that \( n \) begins with 1.) \( a_n = 2 - \dfrac{4}{n} \)
View solution Problem 39
In Exercises 39 - 42, you are given the probability that an event will not happen. Find the probability that the event will happen. \( P(E') = 0.23 \)
View solution Problem 39
In Exercises 19 - 40, use the Binomial Theorem to expand and simplify the expression. \( 2\left(x - 3\right)^4 + 5\left(x - 3\right)^2 \)
View solution Problem 39
In Exercises 35 - 44, write an expression for the \( n \)th term of the geometric sequence. Then find the indicated term. \( a_1 = 100, r = e^x, n = 9 \)
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