Question

# (a) How many three​-digit numbers can be formed from the digits 0 comma 1 comma 2...

(a) How many three​-digit numbers can be formed from the digits 0 comma 1 comma 2 comma 3 comma 4 comma 5 comma 6 comma 7 comma 8 comma and 9

if each digit can be used only​ once?

​(b) How many of these are odd​ numbers?

​(c) How many are greater than 440​?

a) The first digit can be filled by 9 digits i.e. all digits except 0.

The second digit can be filled by 9 digits i.e. all digits except the digit occupied by 1st.

The third digit can be filled by 8 digits.

Total number of three-digit numbers = 9 * 9 * 8 = 648

b) The last digit can be filled 5 digits i.re. all odd digits.

The first digit can be filled by 8 digits i.e. all digits except the last one and 0.

The second digit can be filled by 8 digits.

Total numbers of 3-digit numbers which are odd = 5 * 8 * 8 = 320

c) Total 3-digit numbers greater than 500 = 5 * 9 * 8 = 360

Total 3-digit numbers between 440 and 500 = 1 * 5 * 8 = 40

Total numbers which are greater than 440 = 360 + 40 = 400

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