#(7!)/((2!)^3) = 630#

#"In general when we arrange n items, where there are k different"#

#"items that occur each "n_i" times, for "i=1,2,...,k", then we"#

#"have"#

#(n!)/((n_1)!(n_2)!...(n_k)!)#

#"possibilities of arranging them."#

#"So we need to count how many times the items occur :"#

#"Here we have 7 items : two 579 and one 6, so"#

#(7!)/(2!2!2!1!) = 630 " possibilities"#

#"This is called a multinomial coefficient."#

#"The philosophy behind it is simple. We would have n! ways of"#

#"arranging them if they were different, but the identical items"#

#"can be arranged in "n_i!" ways, without affecting the outcome"#

#"so we divide through all the "(n_i)!.#