If there are 8 T's there are 8 C's, so we are left with 14 slotsThis means that A=G=7P[8 T's]=(308)(228)(147)(0.29)7(0.23)8(0.27)7(0.21)8
Now the problem might actually mean there are at least 8 T's. In which case we'd modify above to be
15∑t=8 (30t)(30−tt)(30−2t15−t)(0.29)15−t(0.23)t(0.27)15−t(0.21)t