InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Let m (respectively, n) be the number of 5-digit integers obtained by using the digits 1,2,3,4 ,5 with repetitions (respectively, without repetitions) such that the sum of any two adjacent digits is odd. Then `m/n` is equal toA. 9B. 12C. 15D. 18 |
|
Answer» Correct Answer - C Digits are 1,2,3,4,5 `{:(,"Even digits = 2,4",,,"number of Even digits = 2"),(,"Totalmarks = 2375",,,"number of Odd digits = 3"):}` Sum of any 2 adhacent digits is odd `rArr` Odd and even digits will alternate Case I For n, Repetition is not allowed `rArrOEOEO` is the only possibility of arrangement of digits, Where O=Odd digit, Where O = Odd digit, E = Even digit. So number of Arrangements `n=3/Oxx2/Exx2/Oxx1/Exx1/O=12` Case II For m, Repetition is allowed ltbrlt `rArr` Tow possioilities (a) OEOEO Number of such arrangements `=3/Oxx2/Exxx3/Oxx2/Exx3/O=108` (b) EOEOE Number of such arrangements `=2/Exx3/Oxx2/Exx3/Oxx2/E=72` So m = 108 + 72 = 180 `m/n=180/12=15` |
|