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Question Number 142947 by mathdanisur last updated on 07/Jun/21

What is the probability that 3 points  will fall twice when a dice is thrown  4 times?

$${What}\:{is}\:{the}\:{probability}\:{that}\:\mathrm{3}\:{points} \\ $$$${will}\:{fall}\:{twice}\:{when}\:{a}\:{dice}\:{is}\:{thrown} \\ $$$$\mathrm{4}\:{times}? \\ $$

Commented by mr W last updated on 07/Jun/21

p=((C_2 ^4 ×5×5)/6^4 )=((25)/(216))

$${p}=\frac{{C}_{\mathrm{2}} ^{\mathrm{4}} ×\mathrm{5}×\mathrm{5}}{\mathrm{6}^{\mathrm{4}} }=\frac{\mathrm{25}}{\mathrm{216}} \\ $$

Commented by mathdanisur last updated on 07/Jun/21

thanks Sir

$${thanks}\:{Sir} \\ $$

Commented by mathdanisur last updated on 07/Jun/21

Sir, C_2 ^4  or C_4 ^2  ?

$${Sir},\:{C}_{\mathrm{2}} ^{\mathrm{4}} \:{or}\:{C}_{\mathrm{4}} ^{\mathrm{2}} \:? \\ $$

Commented by mr W last updated on 08/Jun/21

the same.

$${the}\:{same}.\: \\ $$

Commented by Olaf_Thorendsen last updated on 08/Jun/21

In France we write C_k ^n .  In UK we write C_n ^k .  But it is the same.

$$\mathrm{In}\:\mathrm{France}\:\mathrm{we}\:\mathrm{write}\:\mathrm{C}_{{k}} ^{{n}} . \\ $$$$\mathrm{In}\:\mathrm{UK}\:\mathrm{we}\:\mathrm{write}\:\mathrm{C}_{{n}} ^{{k}} . \\ $$$$\mathrm{But}\:\mathrm{it}\:\mathrm{is}\:\mathrm{the}\:\mathrm{same}. \\ $$

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