Question 117046

Find the number of distinguishable permutations of the group of letters: {{{A}}},{{{A}}},{{{G}}},{{{E}}},{{{E}}},{{{E}}},{{{M}}}.

	Here are the frequencies of the letters: {{{A=2}}}, {{{G=1}}}, {{{E=3}}}, {{{M=1}}} for a total of {{{7}}} letters.

{{{n = 7}}}
Then the number of distinguishable permutations will be:

{{{n!/((n1!)(n2!)(n3!)(n4!))}}}

{{{7!/((2!)(1!)(3!)(1!))}}}


{{{1*2*3*4*5*6*7/((1*2)(1)(1*2*3)(1))}}}

{{{1*2*3*4*5*6*7/(2*6))}}}……… do some simplification

{{{1*3*4*5*7}}}

{{{420)}}}
	
so, the number of distinguishable permutations of the group of letters is {{{420}}}.