To find the number of ways to choose the group, we use combinations for each voice part:

1. Choose 10 sopranos from 13: \(\binom{13}{10}\)

2. Choose 9 altos from 12: \(\binom{12}{9}\)

3. Choose 4 tenors from 6: \(\binom{6}{4}\)

4. Choose 4 basses from 7: \(\binom{7}{4}\)

The total number of ways to choose the group is the product of these combinations:

\(\binom{13}{10} \times \binom{12}{9} \times \binom{6}{4} \times \binom{7}{4}\)

Calculating each combination:

\(\binom{13}{10} = 286\)

\(\binom{12}{9} = 220\)

\(\binom{6}{4} = 15\)

\(\binom{7}{4} = 35\)

Thus, the total number of ways is:

\(286 \times 220 \times 15 \times 35 = 33,033,000\)