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 to

Options

A. 9
B. 12
C. 15
D. 18

Answer

C

Explanation

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`