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The total number of five-digit numbers ofdifferent digits in which the digit in the middle is the largest isa. `sum_(n=4)^9^n P_4`b. `33(3!)`c. `30(3!)`d.none of theseA. `30xx30!`B. `33xx3!`C. `sum_(n=4)^(9)""^(n)C_(4)xx4!`D. none of these |
Answer» The largest digit in the middle of the five digit number can be 4 (when numbers are formed with digits 0, 1, 2, 3, 4), 5 (when 0, 1, 2, 3, 4, 5 are used),…..,9 (when 0, 1, 2,……,9 are used). `:.` Number of five digit numbers with largest digit 5 in the middle `=(""^(4)C_(4)xx4!-""^(3)C_(3)xx3!)` Number of five digit numbers with lardest digit 5 in the middle `=(""^(5)C_(4)xx4!-""^(3)C_(3)xx3!)` Hence, required number of numbers `=(""^(4)C_(4)xx4!-""^(3)C_(3)xx3!)+(""^(5)C_(4)xx4!-""^(4)C_(3)xx3!)` `+(""^(6)C_(4)xx4!-""^(5)C_(3)xx3!)+.....+(""^(9)C_(4)+4!-""^(8)C_(3)xx3!)` |
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