Scrabble?! BINOMIALLY

Is binomially valid for Scrabble? Words With Friends? Lexulous? WordFeud? Other games?
Scrabble (US/Canada)
Yes! (67 pts)
Yes! (56 pts)
Yes! (67 pts)
Yes! (67 pts)
Yes! (68 pts)
Yes! (10 pts)
Yes! (67 pts)
Yes! (68 pts)

Definitions of BINOMIALLY in various dictionaries:

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own boolean-valued outcome: a random variable containing a single bit of information: success/yes/true/one (with probability p) or failure/no/false/zero (with probability q = 1 − p). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment and a sequence of outcomes is called a Bernoulli process; for a single trial, i.e., n = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical significance. The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N. If the sampling is carried out without replacement, the draws are not independent and so the resulting distribution is a hypergeometric distribution, not a binomial one. However, for N much larger than n, the binomial distribution remains a good approximation, and is widely used.

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There are 10 letters in BINOMIALLY ( A1B3I1L1M3N1O1Y4 )

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