Question

(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?

Answer #1

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

how
many odd numbers can be formed from the digits 0,1,2,3,4,5,6 if
each digit can be used only once?

Six-digit numbers are to be formed using only the digits in the
set:
A = {1, 2, 3, 4, 5, 6, 7, 8}
How many such numbers can be formed if repetitions of the
digits are allowed?
In part (a), how many of the numbers contain at least one 3 and
at least one 5?
c. How many 6-digit numbers can be formed if each digit in A can
be used at most once?

how
many four digit numbers can be formed from digits 1, 3, 5, 7 ,8 and
9.; if the numbers are less than 3000 th digits are not used
repeadetly.

How many four-digit numbers can be formed from the digits 1,
3, 5, 7, 8, and 9 if the numbers are less than 3,000 and digits are
not used repeatedly? ( Hint: Begin with the digit where there is a
restriction on the choices.)

How many 4-digit numbers can be formed from the digits 2, 3, 8
and 9?

How many possible 5 digit numbers can be formed with the 10
digits 0 to 9 if repetitions are not allowed and zero cannot be the
first digit?

10. Three-digit numbers are to be made from the 10 digits 0, 1,
2, …, 9. (Assume that the first digit cannot be 0.)
a. How many numbers can be made if repetitions are not allowed
and the number must be divisible by 10?
b. How many numbers can be made if repetitions are allowed and
the number must be even?
c. How many numbers can be made if repetitions are not allowed
and the number must be odd and...

A three-digit numeral is formed by selecting digits from {0, 3,
7, 9} without repetition.
Find the probability that the number formed is:
More than 300
Less than 750
Contains only odd digits
An even number.

(a) How many numbers can be formed by arranging the digits 1, 2,
2, 4, 6, 6, 6?
(b) How many numbers greater than 3,000,000 can be formed by
arranging the digits 1, 2, 2, 4, 6, 6, 6?

How many six-digit numbers have three even digits and three odd
digits?

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