Five people are to be arranged in a row for a group photograph. How many arrangements are there if a married couple in the group insist on sitting next to each other?

A student has 5 courses to take from Mathematics and physics. There are 4 courses in Mathematics and 3 in Physics which he can choose his courses so that he takes exactly two courses in Physics?

If 2257 is the result of subtracting 4577 from 7056 in base n, find n

Find correct to 3 decimal places (\(\frac{1}{0.05} \div\frac{1}{5.005}\)) - (0.05 x 2.05)