Exchange Energy : Cause of Extra Stability of Half-filled & Completely Filled Orbitals

Exchange Energy : Cause of Extra Stability of Half-filled & Completely Filled Orbitals :

In case of  3d⁴ 4s²  configuration in Cr : 
The electron no.1 can exchange its position with electrons nos. 2,3 & 4  i.e., in 3 ways. 
The electron no.2 can exchange 2 ways with electrons 3 & 4 (with electron 1 has already been considered). 
The electron no.3 can exchange only in 1 way (as exchanges with electrons 1 & 2 has already been calculated).
 Hence there are 3+2+1=6 ways of exchange are possible in  3d⁴ arrangement.
Similarly, in 3d⁵ configuration, the total possible ways of exchange is 4+3+2+1=10. 
Therefore, 3d⁵ configuration is more stable than  3d⁴ configuration.