Video Transcript
Find the range of values for 𝑛 that make this a valid expression, 49𝑃𝑛 minus 47.
The notation in this question is for permutations with a general form 𝑟𝑃𝑘, where 𝑟 and 𝑘 must both be nonnegative integers and 𝑟 must be greater than or equal to 𝑘. We can combine these inequalities such that 𝑘 is greater than or equal to zero and less than or equal to 𝑟.
In our expression, 𝑛 minus 47 must be greater than or equal to zero and less than or equal to 49. We can simplify this double inequality by adding 47 to all three parts. Zero plus 47 is 47. When we add 47 to 𝑛 minus 47, we are left with 𝑛. And 49 plus 47 is 96.
Our inequality becomes 𝑛 is greater than or equal to 47 and less than or equal to 96. This is the range of values for 𝑛 for which the expression is valid.
