Step-by-step explanation:
the manager has 25 possibilities to select the team leader.
and that means he/she has then 24 employees left to pick the 3 team members from.
based on the description the sequence of the employees in the team group of 3 does not matter :
e.g. the picks
(employee 11, employee 23, employee 6)
and
(employee 23, employee 6, employee 11)
are in fact the same pick.
so, we are looking for combinations (the sequence does not matter). and not permutations (where the sequence DOES matter).
the possible combinations of 3 employees out of possible 24 are
C(24, 3) = 24!/(3! × (24-3)!) = 24!/(3! × 21!) =
= 24×23×22/(3×2) = 8×23×11 = 2024
so, the total number of ways to arrange such a group is
25 × 2024 = 50,600 ways
