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a 9-character numeric passcode is constructed at random. if the last number cannot be prime and the first digit cannot be 0, 1, or 7, how many different codes can be constructed?

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The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation.

Here,  420,000,000 different passcodes can be construct.

What is the permutation ?

  • The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation.
  • Simply said, a permutation is a term that refers to the variety of possible arrangements or orders.
  • The arrangement's order is important when using permutations.
  • An arrangement of items in a specific order is referred to as a permutation.
  • Here, the components of sets are arranged in a linear or sequential order.
  • When an order or sequence of arrangement is required, permutations are used.
  • Combinations are employed when there are just a limited number of feasible groups to find and there is no requirement for the order or sequence of arrangements. For different kinds of objects, permutations are utilized.
  • Combinations are employed for comparable items.

The first digit excludes [0, 1 and 7] , therefore 7 possible values.

The last number cannot be prime

The last digit excludes [2, 3, 5 and 7] therefore 6 possible values

The second to eight digits (7 digits) can have all 10 values

Therefore different codes that can be constructed is 7*10*10*10*10*10*10*10*6 = 7*6*(10^7) = 420,000,000

Hence 420,000,000 different codes can be construct.

To learn more about permutation  refer,

https://brainly.com/question/28443757

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