class_docstr: Multinomial distribution.
  
  This Multinomial distribution is parameterized by `probs`, a (batch of)
  length-`K` `prob` (probability) vectors (`K > 1`) such that
  `tf.reduce_sum(probs, -1) = 1`, and a `total_count` number of trials, i.e.,
  the number of trials per draw from the Multinomial. It is defined over a
  (batch of) length-`K` vector `counts` such that
  `tf.reduce_sum(counts, -1) = total_count`. The Multinomial is identically the
  Binomial distribution when `K = 2`.
  
  #### Mathematical Details
  
  The Multinomial is a distribution over `K`-class counts, i.e., a length-`K`
  vector of non-negative integer `counts = n = [n_0, ..., n_{K-1}]`.
  
  The probability mass function (pmf) is,
  
  ```none
  pmf(n; pi, N) = prod_j (pi_j)**n_j / Z
  Z = (prod_j n_j!) / N!
  ```
  
  where:
  * `probs = pi = [pi_0, ..., pi_{K-1}]`, `pi_j > 0`, `sum_j pi_j = 1`,
  * `total_count = N`, `N` a positive integer,
  * `Z` is the normalization constant, and,
  * `N!` denotes `N` factorial.
  
  Distribution parameters are automatically broadcast in all functions; see
  examples for details.
  
  #### Pitfalls
  
  The number of classes, `K`, must not exceed:
  - the largest integer representable by `self.dtype`, i.e.,
    `2**(mantissa_bits+1)` (IEE754),
  - the maximum `Tensor` index, i.e., `2**31-1`.
  
  In other words,
  
  ```python
  K <= min(2**31-1, {
    tf.float16: 2**11,
    tf.float32: 2**24,
    tf.float64: 2**53 }[param.dtype])
  ```
  
  Note: This condition is validated only when `self.validate_args = True`.
  
  #### Examples
  
  Create a 3-class distribution, with the 3rd class is most likely to be drawn,
  using logits.
  
  ```python
  logits = [-50., -43, 0]
  dist = Multinomial(total_count=4., logits=logits)
  ```
  
  Create a 3-class distribution, with the 3rd class is most likely to be drawn.
  
  ```python
  p = [.2, .3, .5]
  dist = Multinomial(total_count=4., probs=p)
  ```
  
  The distribution functions can be evaluated on counts.
  
  ```python
  # counts same shape as p.
  counts = [1., 0, 3]
  dist.prob(counts)  # Shape []
  
  # p will be broadcast to [[.2, .3, .5], [.2, .3, .5]] to match counts.
  counts = [[1., 2, 1], [2, 2, 0]]
  dist.prob(counts)  # Shape [2]
  
  # p will be broadcast to shape [5, 7, 3] to match counts.
  counts = [[...]]  # Shape [5, 7, 3]
  dist.prob(counts)  # Shape [5, 7]
  ```
  
  Create a 2-batch of 3-class distributions.
  
  ```python
  p = [[.1, .2, .7], [.3, .3, .4]]  # Shape [2, 3]
  dist = Multinomial(total_count=[4., 5], probs=p)
  
  counts = [[2., 1, 1], [3, 1, 1]]
  dist.prob(counts)  # Shape [2]
  
  dist.sample(5) # Shape [5, 2, 3]
  ```
code: def _log_prob(self, counts):
      return self._log_unnormalized_prob(
          counts
      ) - self._log_normalization(counts)
  
imports: from tensorflow.python.framework import dtypes
  from tensorflow.python.framework import ops
  from tensorflow.python.ops import array_ops
  from tensorflow.python.ops import check_ops
  from tensorflow.python.ops import control_flow_ops
  from tensorflow.python.ops import map_fn
  from tensorflow.python.ops import math_ops
  from tensorflow.python.ops import nn_ops
  from tensorflow.python.ops import random_ops
  from tensorflow.python.ops.distributions import distribution
  from tensorflow.python.ops.distributions import util
  from tensorflow.python.util import deprecation
  from tensorflow.python.util.tf_export import tf_export
label_desc: Use image node_id 10 for calling the Multinomial obj's underlying member method code with example usage: obj._log_prob(counts) and returns: unknown