From among the 36 teachers in a school, one principal and one vice-pri

1.	From among the 36 teachers in a school, one principal and one vice-principal are to be appointed. In how many ways can this be done?
Answer» Given as Total number of teachers in a school = 36 As we know that, number of arrangements of n things taken r at a time = P(n, r) On using the formula, P (n, r) = n!/(n – r)! ∴ Total number of ways in which this can be done = the number of arrangements of 36 things taken 2 at a time = P(36, 2) P (36, 2) = 36!/(36 – 2)! = 36!/34! = (36 × 35 × 34!)/34! = 36 × 35 = 1260 Thus, number of ways in which one principal and one vice-principal are to be appointed out of total 36 teachers in school are 1260.

From among the 36 teachers in a school, one principal and one vice-principal are to be appointed. In how many ways can this be done?

Answer»

Given as

Total number of teachers in a school = 36

As we know that, number of arrangements of n things taken r at a time = P(n, r)

On using the formula,

P (n, r) = n!/(n – r)!

∴ Total number of ways in which this can be done = the number of arrangements of 36 things taken 2 at a time = P(36, 2)

P (36, 2) = 36!/(36 – 2)!

= 36!/34!

= (36 × 35 × 34!)/34!

= 36 × 35

= 1260

Thus, number of ways in which one principal and one vice-principal are to be appointed out of total 36 teachers in school are 1260.