A man needs to form a 5-digit number from the eight digits 1, 3, 4, 5, 6, 7, 8 and 9 without repetition. How many of these 5-digit numbers are (i) less than 40 000?

To solve this problem, we need to consider the place value of each digit in the 5-digit number.

(i) For a 5-digit number to be less than 40,000, the first digit (the ten thousands place) must be either 1 or 3.

Step 1: Choose the first digit There are 2 choices (1 or 3) for the first digit.

Step 2: Choose the second digit After the first digit is chosen, there are 7 remaining digits to choose from for the second digit.

Step 3: Choose the third digit After the first two digits are chosen, there are 6 remaining digits to choose from for the third digit.

Step 4: Choose the fourth digit After the first three digits are chosen, there are 5 remaining digits to choose from for the fourth digit.

Step 5: Choose the fifth digit After the first four digits are chosen, there are 4 remaining digits to choose from for the fifth digit.

So, the total number of 5-digit numbers less than 40,000 that can be formed from the eight digits 1, 3, 4, 5, 6, 7, 8 and 9 without repetition is 27654 = 1680.