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JEE Main Math Class 11 Permutations and Combinations 1 Questions
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© examsnet.com
Question : 5
Total: 100
The sum of all the 4-digit distinct numbers that can be formed with the digits 1, 2,2 and 3 is
[2021, 18 March Shift-I]
26664
122664
122234
22264
Validate
Solution:
Given, digits are
=
1
,
2
,
2
,
3
∴
Total distinct numbers
=
4
!
∕
2
!
=
12
1 at unit place
⇒
Number of such
numbers
=
3
!
2
!
=
3
2 at unit place
⇒
Number of such numbers
=
3
!
=
6
3 at unit place
⇒
Number of such numbers
=
3
!
2
!
=
3
∴
Sum of digits at unit place is
3
×
1
+
6
×
2
+
3
×
3
=
24
Hence, sum of all 4 digit such numbers
=
(
3
+
12
+
9
)
(
10
3
+
10
2
+
10
+
1
)
=
1111
×
24
=
26664
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