Divisibility test of 9 is done by adding digits of the number. If the sum of digits is divisible by 9 then the number is also divisible by 9.
So if 279#4423 is divisible by 9 then the sum of the digits should also be divisible by 9.
Sum of the digits (2+7+9+#+4+4+2+3) = 31+#
31+# is divisible by 9 so # should be 5.
Ad sum of the digits should be 36.
The total possibilities here are 26 but favourable cases are 21 i.e. consonants.
Thus probability = 2126
Let us assume that repetition is allowed as there is no mention of repetition not being allowed. So for the five letter identity code, first four are chosen from the total of 26 alphabets and the fifth letter is always a consonant, so fifth one is chosen from 21 consonants.
Total possibilities are as follows:
26C1 x 26C1 x 26C1 x 26C1 x 21C1 = 26 x 26 x 26 x 26 x 21 = 264 x 21
Total age= 11 x 22 = 242
Age of coach=x
242+x= 23 x 12
x = 276 – 242 = 34 years
25 x 32 x 55 x 7
No. of factors = 13