(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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