Answer: 0.1937
Explanation:
Given : A bowl contains 20 candies; 15 are chocolate and 5 are vanilla.
If we select 5 candies, then the number of ways to select them is given by permutations.
The number of ways to select 5 candies is given by :-
[tex]^{15}P_5=\dfrac{15!}{(15-5)!}=\dfrac{15\times14\times13\times12\times11\times10!}{10!}=360360[/tex]
The number of ways of selecting any 5 candies out of 20:-
[tex]^{20}P_5=\dfrac{20!}{(20-5)!}\\\\=\dfrac{20\times19\times18\times17\times16\times15!}{15!}\\\\=1860480[/tex]
Now, the probability that all 5 are chocolate :-
[tex]=\dfrac{360360}{1860480}=0.193691950464\approx0.1937[/tex]
Hence, the probability that all 5 are chocolate =0.1937
Answer:
A bowl contains 20 candies; 15 are chocolate and 5 are vanilla.
If we select 5 candies, then the number of ways to select them is given by permutations.
The number of ways to select 5 candies is given by :-
^{15}P_5=\dfrac{15!}{(15-5)!}=\dfrac{15\times14\times13\times12\times11\times10!}{10!}=360360
15
P
5
=
(15−5)!
15!
=
10!
15×14×13×12×11×10!
=360360
The number of ways of selecting any 5 candies out of 20:-
\begin{lgathered}^{20}P_5=\dfrac{20!}{(20-5)!}\\\\=\dfrac{20\times19\times18\times17\times16\times15!}{15!}\\\\=1860480\end{lgathered}
20
P
5
=
(20−5)!
20!
=
15!
20×19×18×17×16×15!
=1860480
Now, the probability that all 5 are chocolate :-
=\dfrac{360360}{1860480}=0.193691950464\approx0.1937=
1860480
360360
=0.193691950464≈0.1937
Hence, the probability that all 5 are chocolate
