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how many five letter codes can be made if no letter can be used twice

How Many Five Letter Codes Can Be Made If No Letter Can Be Used Twice class=

Sagot :

The aritmetic sequence has the characteristic that each term is the term before plus a constant number. Then we can create the following system of equations:

[tex]\begin{gathered} x-34=p \\ 345-p=x \end{gathered}[/tex]

where p is the constant value which is added in each term, and x the number between 34 and 345. If we replace the value of "x" from the second equation into the first one:

[tex]\begin{gathered} 345-p-34=p \\ 311=2p \\ 155.5=p \end{gathered}[/tex]

Finally, the term betwen 34 and 345 is 34+p, 189.5

Hence the answer is 189.5