As given a+b+c+d=3 or 5 or 7 or 11 if sum =3 (1+x+x2+...+x4)4→x3 (1−x5)4(1−x)−4→x3 ∴4+3−1C3=6C3=20 If sum=5 (1−4x5)(1−x)−4→x5 ⇒4+5−1C5−4x4.4+0−1C0=8C5−4=52 If sum =7 (1−4x5)(1−x)−4→x7 ⇒4+5−1C4−4.4+0−1C0=8C5−4=52 If sum =11 (1−4x5+6x10)(1−x)−4→x11 ⇒4+11−1C11−4⋅4+6−4C6+6⋅4+1−1C1 =14C11−4⋅9C6+6.4=364−336+24=52 ∴ Total matrices =20+52+80+52=204