In how many ways 4 boys and 3 girls can be seated in a row so that they are alternate.
Let the Arrangement be,
B G B G B G B
4 boys can be seated in 4! Ways.
Girl can be seated in 3! Ways.
Required number of ways,
= 4!*3! = 144.
In how many ways 2 directors and 3 executives can be arranged for a meeting? If there are 6 chairs available two on one side and remaining four on the other side of the table and the two directors has to be together on one side and the executives on the other side.
3 executives in 4 chairs = 4P3 ways
Total no. of ways = 2! * 4P3
A lady arranges a dinner party for 6 guests .The number of ways in which they may be selected from among 10 friends if 2 of the friends will not attend the party together is
Let the friends be A,B,C,D,E,F,G,H,I,J and assume A and B will not battend together
Case 1 : Both of them will not attend the party : Now we have to select the 6 guests from the remaing 8 members
Then no of ways is 8C6 = 28 ways.
Case 2 : Either of them are selected for the party :Now we have to select the 5 guests from the remaing 8 members and one from A and B
Then the no of ways = 2C1 x 8C5 =112 ways.
Therefore total number of ways is 28+ 112 = 140 ways,
What is the value of npo
=> n!/n! = 1
Find the value of n if nP1 = 10
nPr = 10
nPr = n!/(n-r)!
10 = n!/(n-1)!
10 = [n!.(n-1)!]/(n-1)!
n! = 10
Number of signals that can be made using 2 flags out of given 4 flags.
No. of ways of selecting two flags out of four = 4C2
So, total possible different signals generated = 4C2×2!
What is the value of npn
5 singers are to be given performance in a concert. How many ways can they be arranged in a order
5P5 ⇒ 5!/(5-5)!
= 5!/1 ⇒ 5!
= 120 ways
What is the value of 0!
The value of 0! = 1