Question

55 Type the correct answer in the box. Write your answer as a fraction, using / for the fraction bar. Distinct four-letter sequences are formed by picking 4 letter tiles from a bag containing 11 different alphabet tiles. Note that the order in which the letters are picked matters. The probability of getting a particular four-letter sequence is

Answer 1

Solution

The total possible number of ways is

$\begin{gathered} P(11,4)=\frac{11!}{(11-4)!} \\ \\ P(11,4)=\frac{11!}{7!} \\ \\ P(11,4)=\frac{11\times10\times9\times8\times7!}{7!} \\ \\ P(11,4)=11\times10\times9\times8 \\ \\ P(11,4)=7920 \\ \\ Note:\text{ } \\ P(n,r)=\frac{n!}{(n-r)!},\text{ which is the permutation of n objects selecting r} \end{gathered}$

The probability of getting a particular four-letter sequence is

$\frac{1}{7920}$