A touring party of cricket players is made up of six players from each of India, Pakistan and Sri Lanka and 3 from Bangladesh.
li) How
many
different selections of 11 players can be made for a team?
In one match, it is decided to have three players from each of India,
Pakistan and Sri Lanka and two from Bangladesh. How many different
team selections can now be made?

16

Step-by-step explanation:

We must find integers x, y with the most amount of prime divisors, not necessarily distinct, such that x + 3y < 1,000.

Obviously, this is achieved when the divisor is the least prime 2. So, we must find integers n, m such that

since , then n must be 9. For n=9 we find the greatest integer m such that  

and we find m=7

 and   ,  are the numbers we are looking for and the sum of their length is 9+7 = 16.

So, 16 is the maximum possible sum of the length of x and the length of y.