Questions
The total number of 5-digit numbers of different digits in which the digit in the middle is the largest is
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a
∑n=49 nP4−n−1P3
b
∑n=49 P4 n
c
∑n=49 n−1P3
d
None of these
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Correct option is A
The smallest number, which can occur in the middle is 4. The number of numbers with 4 in the middle=4P4−3P3.(∴ The other four places are to be filled by 0, 1, 2 and 3, and a number can not begin with 0)Similarly, the number of numbers with 5 in the middle = 5P4−4P3, etc.∴ The required number of numbers= 4P4−3P3+ 5P4−4P3+ 6P4−5P3+…+ 9P4−8P3=∑n=49 nP4−n−1P3Similar Questions
The number of numbers greater than 106 that can be formed using the digits of the number 2334203, if all the digits of the given number must be used, is
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