---
id: 5900f4af1000cf542c50ffc1
title: 'Problem 322: Binomial coefficients divisible by 10'
challengeType: 5
forumTopicId: 301979
dashedName: problem-322-binomial-coefficients-divisible-by-10
---

# --description--

Let $T(m, n)$ be the number of the binomial coefficients ${}^iC_n$ that are divisible by 10 for $n ≤ i < m$ ($i$, $m$ and $n$ are positive integers).

You are given that $T({10}^9, {10}^7 - 10) = 989\\,697\\,000$.

Find $T({10}^{18}, {10}^{12} - 10)$.

# --hints--

`binomialCoefficientsDivisibleBy10()` should return `999998760323314000`.

```js
assert.strictEqual(binomialCoefficientsDivisibleBy10(), 999998760323314000);
```

# --seed--

## --seed-contents--

```js
function binomialCoefficientsDivisibleBy10() {

  return true;
}

binomialCoefficientsDivisibleBy10();
```

# --solutions--

```js
// solution required
```