From among the 36 teachers in a school, one principal and one vic… - Vidyadip

Question

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

The total number of teachers in a school = 36 One principal and one uice-principal are to be appointed. $\therefore$ Total of ways = Number of arrangement of 36 things taken two at a time $=\ ^{36}\text{P}_2$$=\frac{36!}{(36-2)!}$
$=\frac{36!}{34!}$
$=\frac{36\times35\times34!}{34!}$
$=36\times35$
$=1260$
Hence, Total number of ways to appoint one principal and one vice-principal are 1260.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "(Each question 2 marks)" from Permutations→Permutations — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Show the of the following progression is G.P. Also, find the common ratio in case:$\frac12,\frac13,\frac29,\frac{4}{27}\dots$

The numbers 1, 2, 3 and 4 are written separately on four slips of paper. The slips are then put in a box and mixed thoroughly. A person draws two slips from the box, one after the other, without replacement. Describe the following events: A = The number on the first slip is larger than the one on the second slip. B = The number on the second slip is greater than 2. C = The sum of the numbers on the two slips is 6 or 7. D = The number on the second slips is twice that on the first slip. Which pair(s) of events is (are) mutually exclusive?

Find the equations of the lines parallel to y axis and passing through (– 2, 3).

A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random, find the probability that:

Both the balls are white
One ball is black and the other red
Both the balls are of the same colour.

For each of the following compound statements first identify the connecting words and then break it into component statements. Square of an integer is positive or negative.

How many different numbers of six digits can be formed from the digits 3, 1, 7, 0, 9, 5 when repetition of digits is not allowed?

Convert the following products into factorials: 5.6.7.8.9.10

How many 3-digit even numbers can be formed, from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?

The sum of three numbers which are consecutive terms of an A.P. is $21$. If the second number is reduced by $1$ and the third is increased by $1$, we obtain three consecutive terms of a G.P. Find the numbers.

Which of the following statements are true and which are false? In each case give a valid reason for saying so. r: Circle is a particular case of an ellipse.