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Find the number of arrangements of all the letters of the word LANCERS that satisfy each of the following conditions. The letters R and S

Find the number of arrangements of all the letters of the word LANCERS that satisfy each of the following conditions.

  1. The letters R and S must be together.
  2. The letter R and S are not together.

You are setting up a system of programming codes for a universal TV Remote. Each code will have 5 digits and cannot include a 0 or repeat any digits. How many codes:

a) begin with an odd number?

b) begin and end with an even number?

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