How many numbers can be formed with the digits 1, 6, 7, 8, 6, 1 so that the odd digits always occupy the odd places Choose the correct choice:
A) 15
B) 12
C) 18
D) 20
E) 22
Solution   The digits are 1, 6, 7, 8, 7, 6, 1. In this seven-digit no.there are four odd places and three even places OEOEOEO. The four odd digits 1, 7, 7, 1 can be arranged in four odd places in [4!/2!×2] = 6 ways [as 1 and 7 are both occurring twice].   The even digits 6, 8, 6 can be arranged in three even places in 3!/2! = 3 ways.   Total no. of ways = 6 × 3 = 18   Answer 18
<result>C</result>
How many numbers can be formed with the digits 1, 6, 7, 8, 6, 1 so that the odd digits always occupy the odd places