Jim enters a candy shop which has N different types of candies, each candy is of the same price. Jim has enough money to buy K candies. In how many different ways can he purchase K candies if there are infinite candies of each kind?
The first line contains an integer T, the number of tests.
This is followed by 2T lines which contain T tests:
The first line (of each testcase) is an integer N and the second line (of each testcase) is an integer K.
For each testcase, print the number of ways Jim can buy candies from the shop in a newline. If the answer has more than 9 digits, print the last 9 digits.
This problem may expect you to have solved nCr Table
1 <= T <= 200
1 <= N < 1000
1 <= K < 1000
2 4 1 2 3
There are 2 testcases, for the first testcase we have N = 4 and K = 1, as Jim can buy only 1 candy, he can choose to buy any of the 4 types of candies available. Hence, his answer is 4. For the 2nd testcase, we have N = 2 and K = 3, If we name two chocolates as a and b, he can buy
aaa bbb aab abb
chocolates, hence 4.
Solution in Python
def fact(x,y=0): p = 1 for i in range(y+1,x+1): p*=i return p for _ in range(int(input())): n = int(input()) k = int(input()) print((fact(k+n-1,n-1)//fact(k))%10**9)