The correct option is C 758
The letters are:
P R O T I N
P R O
O
Thus, number of permutations taken 4 at a time is the coefficient of x4 in:
4!×(1+x1!+x22!+x33!).(1+x1!+x22!)2.(1+x1!)3=>(6+6x+3x2+x3).(2+2x+x2)2.(1+x)3=>(6+6x+3x2+x3).(4+8x2+x4+8x+4x3).(1+3x+3x2+x3)=>{(6+24+24+8)+(24+48+24+4).3+(48+48+12).3+(48+24)}=(62+300+324+72)=758
Hence, (c) is correct.