document.write( "Question 1155262: Using the digits from the set 012345 and six find the amount of odd three digit numbers that can be created \n" ); document.write( "
Algebra.Com's Answer #777834 by Edwin McCravy(20055)![]() ![]() You can put this solution on YOUR website! \r\n" ); document.write( "To be odd, the last digit must be odd, that is, it must be 1,3, or 5.\r\n" ); document.write( "To have three digits the first digit cannot be 0.\r\n" ); document.write( "\r\n" ); document.write( "We choose the most restrictive digit first, which is the last one.\r\n" ); document.write( "\r\n" ); document.write( "We can choose the last digit any of 3 ways.\r\n" ); document.write( "\r\n" ); document.write( "Now we choose the next most restrictive digit, which is the first one.\r\n" ); document.write( "\r\n" ); document.write( "That leaves 4 possible choices for the first digit, 2,4 and the two\r\n" ); document.write( "odd digits besides the one chosen for the last digit.\r\n" ); document.write( "So there are 3∙4=12 ways to choose the last and first digits.\r\n" ); document.write( "\r\n" ); document.write( "The middle digit is the least restrictive one, so we choose it last.\r\n" ); document.write( "\r\n" ); document.write( "So we finally choose the middle digit as any of the 4 digits besides the two\r\n" ); document.write( "digits chosen for the first and last digits.\r\n" ); document.write( "answer = 3∙4∙4 = 48 odd three-digit numbers. \r\n" ); document.write( "\r\n" ); document.write( "Here are all 48:\r\n" ); document.write( "\r\n" ); document.write( " 1. 103\r\n" ); document.write( " 2. 105\r\n" ); document.write( " 3. 123\r\n" ); document.write( " 4. 125\r\n" ); document.write( " 5. 135\r\n" ); document.write( " 6. 143\r\n" ); document.write( " 7. 145\r\n" ); document.write( " 8. 153\r\n" ); document.write( " 9. 201\r\n" ); document.write( "10. 203\r\n" ); document.write( "11. 205\r\n" ); document.write( "12. 213\r\n" ); document.write( "13. 215\r\n" ); document.write( "14. 231\r\n" ); document.write( "15. 235\r\n" ); document.write( "16. 241\r\n" ); document.write( "17. 243\r\n" ); document.write( "18. 245\r\n" ); document.write( "19. 251\r\n" ); document.write( "20. 253\r\n" ); document.write( "21. 301\r\n" ); document.write( "22. 305\r\n" ); document.write( "23. 315\r\n" ); document.write( "24. 321\r\n" ); document.write( "25. 325\r\n" ); document.write( "26. 341\r\n" ); document.write( "27. 345\r\n" ); document.write( "28. 351\r\n" ); document.write( "29. 401\r\n" ); document.write( "30. 403\r\n" ); document.write( "31. 405\r\n" ); document.write( "32. 413\r\n" ); document.write( "33. 415\r\n" ); document.write( "34. 421\r\n" ); document.write( "35. 423\r\n" ); document.write( "36. 425\r\n" ); document.write( "37. 431\r\n" ); document.write( "38. 435\r\n" ); document.write( "39. 451\r\n" ); document.write( "40. 453\r\n" ); document.write( "41. 501\r\n" ); document.write( "42. 503\r\n" ); document.write( "43. 513\r\n" ); document.write( "44. 521\r\n" ); document.write( "45. 523\r\n" ); document.write( "46. 531\r\n" ); document.write( "47. 541\r\n" ); document.write( "48. 543\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |