How many different committees can be formed from 11 teachers and 41 students if the committee consists of 4 teachers and 3 students? . in how many ways can the committee of 7 members be selected?

The number of combinations of teachers selected 4 at a time is 11C4. The number of combinations of students selected 3 at a time is 41C3 The number of ways of selecting the committee of 7 is given by: 11!/4!7!×41!/3!38!
=11×10×9×8/4×3×2×1×  41×40×39/3×2×1
=506503200/144
=3517383