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In the figure, two 4-digit numbers are to be formed by filling the places with digits. The number of different ways in which the places can be filled by digits so that the sum of the numbers formed is also a 4-digit number and in no place the addition is with carrying is
- a)554
- b)220
- c)454
- d)none of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
In the figure, two 4-digit numbers are to be formed by filling the pla...
If 0 is placed in the units place of the upper number then the units pice of the lower number can be filled in 10 ways (Filling by ay one of 0, 1, 2......9).
If 1 placed in the units placed of the upper number then the unit place of the lower number can be filled in 9 ways (filling by any one of 0, 1, 2, ..., 8), etc.
the units column can be filled in 10 - 9 + 8 + ... * 1, i.e., 55 ways. Similarly for the second and the third column. The number of ways for the fourth column = 8 + 7 + ... + 1 = 36
∴ the required number of ways = 55 x 55 x 55 x 36
If 1 placed in the units placed of the upper number then the unit place of the lower number can be filled in 9 ways (filling by any one of 0, 1, 2, ..., 8), etc.
the units column can be filled in 10 - 9 + 8 + ... * 1, i.e., 55 ways. Similarly for the second and the third column. The number of ways for the fourth column = 8 + 7 + ... + 1 = 36
∴ the required number of ways = 55 x 55 x 55 x 36
Most Upvoted Answer
In the figure, two 4-digit numbers are to be formed by filling the pla...
If 0 is placed in the units place of the upper number then the units pice of the lower number can be filled in 10 ways (Filling by ay one of 0, 1, 2......9).
If 1 placed in the units placed of the upper number then the unit place of the lower number can be filled in 9 ways (filling by any one of 0, 1, 2, ..., 8), etc.
the units column can be filled in 10 - 9 + 8 + ... * 1, i.e., 55 ways. Similarly for the second and the third column. The number of ways for the fourth column = 8 + 7 + ... + 1 = 36
∴ the required number of ways = 55 x 55 x 55 x 36
If 1 placed in the units placed of the upper number then the unit place of the lower number can be filled in 9 ways (filling by any one of 0, 1, 2, ..., 8), etc.
the units column can be filled in 10 - 9 + 8 + ... * 1, i.e., 55 ways. Similarly for the second and the third column. The number of ways for the fourth column = 8 + 7 + ... + 1 = 36
∴ the required number of ways = 55 x 55 x 55 x 36
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Community Answer
In the figure, two 4-digit numbers are to be formed by filling the pla...
If 0 is placed in the units place of the upper number then the units pice of the lower number can be filled in 10 ways (Filling by ay one of 0, 1, 2......9).
If 1 placed in the units placed of the upper number then the unit place of the lower number can be filled in 9 ways (filling by any one of 0, 1, 2, ..., 8), etc.
the units column can be filled in 10 - 9 + 8 + ... * 1, i.e., 55 ways. Similarly for the second and the third column. The number of ways for the fourth column = 8 + 7 + ... + 1 = 36
∴ the required number of ways = 55 x 55 x 55 x 36
If 1 placed in the units placed of the upper number then the unit place of the lower number can be filled in 9 ways (filling by any one of 0, 1, 2, ..., 8), etc.
the units column can be filled in 10 - 9 + 8 + ... * 1, i.e., 55 ways. Similarly for the second and the third column. The number of ways for the fourth column = 8 + 7 + ... + 1 = 36
∴ the required number of ways = 55 x 55 x 55 x 36
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In the figure, two 4-digit numbers are to be formed by filling the places with digits. The number of different ways in which the places can be filled by digits so that the sum of the numbers formed is also a 4-digit number and in no place the addition is with carrying isa)554b)220c)454d)none of theseCorrect answer is option 'D'. Can you explain this answer?
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