Consider the digit 1,2,3,....,7. In how many ways four digits numbers can be formed if they are between 2000 and 5000 and repetitions are allowed
Answers
Answer:
P_Total there are 6 digits, from which we have to form 4 digits number.
We need to choose 4 digits randomly and form a number without repeating any digit.
In this process, we need to determine the number of possibilities where order does not matter.
So, we use the permutation formula and that is
n
P
r
=
(n−r)!
n!
, where n is the total number of objects and r is the number of objects taken at a time.
Given, n=6 and r=4
∴
6
P
4
=
(6−4)!
6!
=
2!
6!
=
2!
6×5×4×3×2!
=6×5×4×3
=360
∴
6
P
4
=360
∴ In 360 ways the 4-digits numbers can be form using the digits 1,2,3,7,8,9.
From these, the even numbers must contain the last digit as 2 or 8.
If we fix 2 or 8 at 4
th
place, then there are
5
P
3
ways for each.
∴ Total number of even numbers =2×
5
P
3
=2×
(5−3)!
5!
=2×
2!
5!
=2×
2×1
5×4×3×2×1
=120
∴ there are total 120 even numbers.
Answer:
∴ there are total 120 even numbers
Step-by-step explanation:
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