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The sum of the digits in the digits unit place of all the numbers formed with the help of 3,4,5,6 taken all at a time is :
- a)432
- b)108
- c)36
- d)18
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The sum of the digits in the digits unit place of all the numbers form...
We can arrange this number in 4! way i.c. 24 way and each digit appear 3! times at each place, so each number come on unit place 6 time so sum = (3 + 4 + 5 +6) * 6
= 18 x 6 = 108
= 18 x 6 = 108
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The sum of the digits in the digits unit place of all the numbers form...
Question:
The sum of the digits in the digits unit place of all the numbers formed with the help of 3, 4, 5, 6 taken all at a time is:
a) 432
b) 108
c) 36
d) 18
Answer:
To find the sum of the digits in the unit place of all the numbers formed with the help of 3, 4, 5, and 6 taken all at a time, we need to consider all the possible combinations and calculate the sum.
Step 1: Finding all possible combinations
To form all possible combinations, we can use the concept of permutations. We have 4 digits (3, 4, 5, 6), and we need to take all of them at a time. The total number of permutations can be calculated using the formula for permutation of n objects taken all at a time, which is given by n!.
In this case, the number of permutations is 4!, which is equal to 4 x 3 x 2 x 1 = 24.
Step 2: Calculating the sum of unit digits
We can now calculate the sum of the unit digits for all the 24 numbers formed by taking all the digits at a time.
To simplify the calculation, we can observe that each digit (3, 4, 5, and 6) will appear in the unit place 6 times out of the total 24 permutations. This is because each digit has an equal chance of being in the unit place when forming a 4-digit number.
So, the sum of the unit digits will be:
(3 + 4 + 5 + 6) x 6 = 18 x 6 = 108
Therefore, the correct answer is option b) 108.
The sum of the digits in the digits unit place of all the numbers formed with the help of 3, 4, 5, 6 taken all at a time is:
a) 432
b) 108
c) 36
d) 18
Answer:
To find the sum of the digits in the unit place of all the numbers formed with the help of 3, 4, 5, and 6 taken all at a time, we need to consider all the possible combinations and calculate the sum.
Step 1: Finding all possible combinations
To form all possible combinations, we can use the concept of permutations. We have 4 digits (3, 4, 5, 6), and we need to take all of them at a time. The total number of permutations can be calculated using the formula for permutation of n objects taken all at a time, which is given by n!.
In this case, the number of permutations is 4!, which is equal to 4 x 3 x 2 x 1 = 24.
Step 2: Calculating the sum of unit digits
We can now calculate the sum of the unit digits for all the 24 numbers formed by taking all the digits at a time.
To simplify the calculation, we can observe that each digit (3, 4, 5, and 6) will appear in the unit place 6 times out of the total 24 permutations. This is because each digit has an equal chance of being in the unit place when forming a 4-digit number.
So, the sum of the unit digits will be:
(3 + 4 + 5 + 6) x 6 = 18 x 6 = 108
Therefore, the correct answer is option b) 108.
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Community Answer
The sum of the digits in the digits unit place of all the numbers form...
We can arrange this number in 4! way i.c. 24 way and each digit appear 3! times at each place, so each number come on unit place 6 time so sum = (3 + 4 + 5 +6) * 6
= 18 x 6 = 108
= 18 x 6 = 108
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