Find the sum of all 4−digit numbers that can be formed using the digit 1,3,5,7,9
without repetition
Answers
Answer:
666600
Step-by-step explanation:
Total no. of digits are 5, i.e.,
n=5
Total no. of digits required is 4, i.e.,
r=4
Therefore,
No. of 4 digits no. that can be formed =nPr=5P4=1!5!=120
No. of times each digit will appear =5120=24
Sum of digits at unit place =24(1+3+5+7+9)=24×25=600
Sum of all numbers =600×1000+600×100+600×10+600=666600
Hence the sum off all 4 diit numbers is 666600.
Given : four digit numbers that can be formed by the digits 1 3 5 7 9 without repetition
To Find : sum of all such four digit numbers
Solution:
1 3 5 7 9
numbers can be formed = ⁵P₄ = 5! = 120 numbers
At each place digit will occur 120/5 = 24 time
Thousand place 100 place Tens place units place
Sum of Digits at each place = 24 ( 1 + 3 + 5 + 7 + 9)
= 24 ( 25)
= 600
Hence sum of all four digit numbers
600 (1000) + 600(100) + 600(10) + 600(1)
= 600 ( 1000 + 100 + 10 + 1)
= 600 ( 1111)
= 666600
sum of all four digit numbers that can be formed by the digits 1 3 5 7 9 without repetition is 666600
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