How many different sequences of 4 digits are possible if the first digit must be 3, 4, or 5 and if the

sequence may not end in 000? Repetition of digits is allowed.

A) 2000 B) 2997 C) 2999 D) 1512

numbers starting with 3,4, or 5 with no other restrictions = 3x10x10x10 = 3000

numbers starting with 3,4, or 5 and ending with 000 = 3x1 = 3

So total numbers as stated = 3000 - 3 = 2997

Well, this is quite a puzzling question, but let's break it down.

Since the first digit must be 3, 4, or 5, we have 3 choices for the first digit.

For the second, third, and fourth digits, we have 10 choices each, since repetition of digits is allowed.

So, the total number of different sequences possible would be 3 choices for the first digit multiplied by 10 choices for each of the three remaining digits.

3 * 10 * 10 * 10 = 3000

But wait! We have to subtract the sequences that end in 000, so we need to remove 1 from the total.

3000 - 1 = 2999

Therefore, the correct answer is option C) 2999.

Just imagine, there are 2999 interesting and unique sequences waiting to be formed! I hope that clears things up for you.

To find the number of different sequences of 4 digits that meet the given conditions, we can count the possibilities for each digit position.

For the first digit, we are given that it must be 3, 4, or 5. So there are 3 possible choices for the first digit.

For the second digit, any digit from 0 to 9 is allowed since repetition is allowed. So there are 10 possible choices for the second digit.

For the third and fourth digits, any digit from 0 to 9 is allowed. However, since the sequence may not end in 000, we need to subtract 1 from the total number of choices. So there are 9 choices for both the third and fourth digits.

To find the total number of sequences, we multiply the number of choices for each digit position:

Total number of sequences = 3 choices for the first digit * 10 choices for the second digit * 9 choices for the third digit * 9 choices for the fourth digit

Total number of sequences = 3 * 10 * 9 * 9 = 2430

However, this calculation includes sequences that have three 0's as the last three digits, which is not allowed. We need to subtract the number of sequences that have three 0's as the last three digits.

Number of sequences with three 0's as the last three digits = 3 choices for the first digit * 1 choice for the second digit * 1 choice for the third digit * 1 choice for the fourth digit

Number of sequences with three 0's as the last three digits = 3 * 1 * 1 * 1 = 3

So, the total number of valid sequences is:

Total number of sequences = 2430 - 3 = 2427

Therefore, the correct answer is not listed among the options given.

write an integer to represent each description