Answer:
The probability of getting a particular four-letter sequence is [tex]\frac{1}{7920}[/tex] or 0.0001262
Step-by-step explanation:
We are given that Distinct four-letter sequences are formed by picking 4 letter tiles
Total number of tiles = 11
Now we are also given that the order in which the letters are picked matters.
So, we will use permutation over here .
Formula : [tex]^nP_r=\frac{n!}{(n-r)!}[/tex]
Now we are given that Distinct four-letter sequences are formed by picking 4 letter tiles from a bag containing 11 different alphabet tiles.
So, n = 11
r = 4
So, The probability of getting a particular four-letter sequence :
= [tex]\frac{1}{^{11}P_4}[/tex]
= [tex]\frac{1}{\frac{11!}{(11-4)!}}[/tex]
= [tex]\frac{1}{\frac{11!}{7!}}[/tex]
= [tex]\frac{1}{7920}[/tex]
=[tex]0.0001262[/tex]
Hence the probability of getting a particular four-letter sequence is [tex]\frac{1}{7920}[/tex] or 0.0001262.
