Answer:

Since the problem is on how a group of 4 people can be selected from a group of 12 people without concerning the order of selection, we can use the combination formula to determine the answer with n=12n=12 and r=4r=4. This yields

Cnr=n!(n−r)!r!C142=12!(12−4)!4!Substitution of values=12!(8)!4!=12×11×10×9×8×7×6×5×4×3×2×1(8×7×6×5×4×3×2×1)(4×3×2×1)Expanding the factorial=12×11×10×94×3×2×1Simplifying by cancelling like terms=11,88024=495Crn=n!(n−r)!r!C412=12!(12−4)!4!Substitution of values=12!(8)!4!=12×11×10×9×8×7×6×5×4×3×2×1(8×7×6×5×4×3×2×1)(4×3×2×1)Expanding the factorial=12×11×10×94×3×2×1Simplifying by cancelling like terms=11,88024=495

Hence, there are 495495 ways to choose a group of 4 people from the main group of 12 people.