In how many ways can the letters of the expression x2y2z4 be arranged when written without using exponents?

To find: number of ways the letters can be arranged


The following table shows the possible arrangements



However, we see that case 1 = is the same as case 4 =


Similarly (case2,case 5), (case 3,case 6) are the same


So there are only 3 distinct cases


Hence the letters can be arranged in 3 distinct ways


1