The sample space of the experiment (i.e. the total number of ways he can pick 7 random pages out of a total of 6 + 4 = 10 pages) is given by:
[tex] ^{10}C_7=120[/tex]
If he picks at least 5 pages of maths homework, this means that he either picked 5 pages or 6 pages of maths homework.
The number of ways he can pick 5 or 6 maths homework is given by:
[tex] ^6C_5+{ ^6C_6}=6\times1=6[/tex]
Therefore, the probability that he recovers at least 5 pages of his math homework is given by:
[tex] \frac{6}{120} = \frac{1}{20} [/tex]
