Answer :
a) Four-digit strings with 10⁴ characters are available.
b) A string that finishes in an odd number has 10 options for the first three digits and 5 options for the last digit.
c) The fourth digit has nine alternatives.
Given,
We have to find the number of strings of four decimal digits for the following conditions;
a) Do not use the same numeral more than once.
There are 10⁴ strings with four decimal digits.
We have 10 options for the first digit, 9 options for the second digit, 8 options for the third digit, and 7 options for the fourth digit when creating a string with 4 different digits. We deduce from the product rule that there are 10 9 8 7 = 5040 four decimal digits with no duplicate digits.
b) End with an odd digit
There are 10 choices (ranging from 0 to 1, 2,..., 9) for the first three digits of a string that ends in an odd number, and 5 possibilities (ranging from 1, 3, 5, 7,.., 9) for the last digit. According to the product rule, there are 5000 strings that terminate in an even number, or 10 × 10 × 10 × 5.
c) Have exactly three digits that are 8
There is one non-8 digit in the 4-decimal string, which includes exactly 3 digits that are 8. Therefore, there are 9 options for the fourth digit (ranging from 0 through 1, 2, 3, 4, 5, 6, and 9). The non-digit may appear in the string at positions 1, 2, 3, or 4. The sum rule leads us to the conclusion that there are 36 four decimal digits with exactly three 8s, which equals 9 + 9 + 9 + 9 = 36.
Learn more about strings of decimal digits here;
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Question is incomplete. Completed question is given below;
How many strings of four decimal digits
a) Do not contain the same digit twice
b) End with an odd digit?
c) Have exactly three digits that are 8
