If the shoes are named
L1 R1 ==> Women 1 (W1)
L2 R2 ==> Women 2 (W2)
L3 R3 ==> Women 3 (W3)
Now all the possible favourable events for the given probability is
[L2 R2 (W1)]×[L3 R3 (W2)]×[L1 R1 (W3)] = 1/9 × 1 × 1/4 = 1/36
[L3 R3 (W1)]×[L1 R1 (W2)]×[L2 R2 (W3)] = 1/9 × 1/4 × 1 = 1/36
[L2 R3 (W1)]×[L3 R1 (W2)]×[L1 R2 (W3)] = 1/9 × 1/2 × 1/2 = 1/36
[L3 R2 (W1)]×[L1 R3 (W2)]×[L2 R1 (W3)] = 1/9 × 1/2 × 1/2 = 1/36
Required Probability = 1/36 + 1/36 + 1/36 + 1/36 = 1/9.