Find the value of r if 7pr =42.

1. Use the permutation formula: \(nPr= \frac { n! } { ( n- r) ! } \)
2. Given \(7Pr= 42\), substitute \(n= 7\):

\(7Pr= \frac { 7! } { ( 7- r) ! } = 42 \)

3. Simplify the factorial:

\(\frac { 7\times 6\times 5\times 4\times 3\times 2\times 1  } { ( 7- r) ! } = 42\)

4. Try \(r= 1\):

\(7P1= \frac { 7! } { ( 7- 1) ! } = \frac { 7! } { 6! } = 7= 42\)

  This is not correct. Therefore, try\(r= 1\)

\(7P1= 7= 7\)

5. Therefore, the correct value of r is 1.

Supplemental Knowledge:

The concept of permutations is crucial in various real-life scenarios such as seating arrangements, creating passwords, and analyzing different possible outcomes in events. For instance, if you have 7 people and you want to know how many different ways you can arrange them in 3 seats, you would use permutations to find the answer.

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