A country has ten smart cities. The government decides to connect all these cities by road. How many roads the government need to construct so that every city is connected to every other city ?
$45$
$50$
$55$
$60$
The number of ways to give away $25$ apples to $4$ boys, each boy receiving at least $4$ apples, are
The number of triplets $(x, y, z)$. where $x, y, z$ are distinct non negative integers satisfying $x+y+z=15$, is
$^{20}C_1 + 3 ^{20}C_2 + 3 ^{20}C_3 + ^{20}C_4$ is equal to-
The number of ways in which five identical balls can be distributed among ten identical boxes such that no box contains more than one ball, is
How many numbers between $5000$ and $10,000$ can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ each digit appearing not more than once in each number