Question #c5675

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Question #c5675

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Answer 1 · 2018-01-05T17:27:27

$\frac{1}{66}$ $1/66$

Explanation:

$ARRANGEMENTS counts 12 letters :$ $"ARRANGEMENTS counts 12 letters :"$
$2 ARNE and 1 GMTS.$ $"2 ARNE and 1 GMTS."$
$So the number of arrangements is :$ $"So the number of arrangements is : "$
$\frac{12!}{{(2!)}^{4} {(1!)}^{4}} = 29937600 (multinomial distribution)$ $(12!)/((2!)^4 (1!)^4) = 29937600 " (multinomial distribution)"$
$The number of arrangements beginning with EE is :$ $"The number of arrangements beginning with EE is :"$
$\frac{10!}{{(2!)}^{3} {(1!)}^{4}} = 453600$ $(10!)/((2!)^3 (1!)^4) = 453600$
$So the odds for an arrangement to begin with EE is :$ $"So the odds for an arrangement to begin with EE is : "$
$\frac{453600}{29937600} = \frac{1}{66} .$ $453600/29937600 = 1/66.$

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Question #c5675

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