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  "body": "\n## Definition\n\nLet $k_1, \\dots, k_m$ be natural numbers and let $n = k_1 + \\dots + k_m$.\nThe multinomial coefficient is the natural number\n$$\\binom{n}{k_1, k_2, \\dots, k_m} = \\frac{n!}{k_1!\\, k_2! \\cdots k_m!}.$$\n\n## Remarks\n\nFor $m = 2$ it is the [[binomial coefficient|092GEF38YD]]: $\\binom{n}{k, n-k} = \\binom{n}{k}$.\nIt counts the ways to put $n$ distinct objects into $m$ labelled boxes, with $k_i$ objects in box $i$.\nIt also counts the distinct words that use a letter $a_i$ exactly $k_i$ times. For example, MISSISSIPPI has $\\frac{11!}{1!\\,4!\\,4!\\,2!} = 34650$ distinct rearrangements.\nIt is the coefficient in the [[multinomial theorem|0XFC1VQYEK]].\n\n## Explanations\n\n### L1 human\n\nThe multinomial coefficient counts the ways to split $n$ objects into groups of given sizes.\nTo split 4 people into a group of 2 and two groups of 1, with labelled groups, there are $\\frac{4!}{2!\\,1!\\,1!} = 12$ ways.\n",
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