MathRevolution wrote:

[GMAT math practice question]

The manager of a certain company gives its employees one rostered day off between Monday and Friday each week. In how many ways can four employees take their leave, if they cannot all be rostered off together?

A. \(120\)

B. \(125\)

C. \(620\)

D. \(625\)

E. \(3125\)

If there were no restriction on leave, then total number of ways 4 employees can take their leaves will be

\(5*5*5*5=625\) (each of the 4 employees has 5 options to choose from)

Number of ways in which all the employees are on leave on the same day\(=5\) ( everybody is on leave on Monday, Tuesday, Wednesday, Thursday or Friday)

Hence number of ways in which leaves can be taken such that not all are restored off together\(=625-5=620\)

Option

C