find the number of permutation and combination of 4 letters taken from the word ARYABHATTA

Explanation

There are 10 letters A,A,A,A,T,T,B,R,H,Y
We have following cases
Cases 1 When all are different i.e. # `triangle square circ` . 4 letters can be arranged in 4! Ways.
Case 2 When two identical and two different # # `triangle circ`
Which can be performed in `""^(2)C_(1).""^(5)C_(2). (4!)/(2!)` ways.
Case 3 When three identical # # `triangle `
`""^(1)C_(1)xx""^(5)C_(1)xx(4!)/(3!)`
Case 4 When two are alike and two are also i.e. # # OO
`""^(2)C_(2) xx (4!)/(2!2!)`
Case 5 When all are identical
`""^(1)C_(1).(4!)/(4!)`
For combination of 4 letters `""^(6)C_(4)+""^(2)C_(1).""^(1)C_(1).""^(5)C_(1)+""^(2)C_(2)+""_(1)C_(1)=42`
For permutation `""^(6)C_(4).4! + ""^(2)C_(1).""_(5)C_(2).(4!)/(4!)+""^(1)C_(1).""^(5)C_(1).(4!)/(3!)+""^(2)C_(2).(4!)/(2!2!)+""^(1)C_(1).(4!)/(4!)=627`