Six X’s have to be placed in squares of the figure given below, such that each row contains at least one X. The number of different ways in which this can be done is

First Method: Number of cross marks in

∴ Required number = 8 + 4 + 6 + 8 = 26

Second Method:

Number of ways of putting six cross marks in 8 squares when there is no restriction ${=}^8{\mathrm{C}}_6=28$.

Number of ways when the six cross marks are put in first and second rows ${=}^6{\mathrm{C}}_6=1$.

Number of ways when the six cross marks are put in second and third rows ${=}^6{\mathrm{C}}_6=1$.

∴ Required number = 28 – 2 = 26.