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How many two digit numbers can be generated using the digits 1,2,3,4 without repeating any digit ?
We have 4 digits i.e 1,2,3,4.
Total no. of ways
There are three places P, Q and R st 3 roads connect to P and Q and 4 roads connect to Q and R. In how many ways can one travel from P to R ?
P to Q : 3 roads.
Q to R : 4 roads.
P to R : ways.
There are 10 women and 15 men in an office. In how many ways a person can be selected ?
There are 10 women and 15 men.
Total no. of ways in which a person can be selected ( Addition theorem)
There are 10 women and 15 men in an office. In how many ways a team of a man and a woman can be selected ?
There are 10 women and 15 men.
Total no. of ways in which a team of a man and a woman can be selected ( Multiplication theorem)
In how many ways three boys can be seated in five chairs ?
There are three boys, 5 chairs.
The 1^{st} boy can sit in any of the five chairs (5 ways).
Similarly 2^{nd} and 3^{rd} boys can sit in the chairs in 4 and 3 ways respectively.
Total no of ways .
There are 6 persons in an office. A groupe of 3 persons has to be fromed. In how many ways can the group be formed ?
Number of ways in which the group can be formed
There are 5 yellow, 4 green and 3 black balls in a bag. All the 12 balls are drawn one by one and arranged in a row. Find out the no. of different arrangements possible ?
In how many ways 7 boys can be seated in a circular order ?
No. of ways 7 boys can be seated in a circular order .
In haw many ways can a team of 5 persons be formed out of a total of 10 persons st two particular persons should be included in each team ?
Two particular persons should be included in each team.
Therefore we have to select remaining persons from persons.
Hence, required no. of ways .
In how many ways can a team of 5 persons be formed out of a total of 10 persons st two particular persons should not be included in any team ?
Here n=10, r=5, s=2.
Hence, no. of ways .
How many triangles can be formed by joining the vertices of a decogon ?
A decagon have 10 vertices.
If there are 9 horizontal lines and 9 vertical lines in a chess board, how many rectagles can be formed in the chess board ?
No. of rectangles that can be formed by using ‘m’ horizontal lines and ‘n’ vertical lines .
Here m=9 and n=9.
Find the no. of diagonals of a decagon ?
No. of diagonals of a polygon of n sides .
Here n=10,
Find the no. of triangles that can be formed using 14 points in a plane st 4 points are collinear ?
Here n=14, m=4.
There are 4 oranges, 5 apples and 6 mangoes in a basket. In how many ways can a person make a selection of fruits among the fruits in the basket ?
Whenever it is not mentioned that fruits are distinct, we take them as identical.
Hence, all 4 oranges, 5 apples, 6 mangoes are identical.
Total no. of ways
What is the sum of all 4 digit numbers formed using the digits 2,3,4 and 5 without repeatation ?
Sum of all distinct numbers formed .
Here n=4,
In a birthday party, every person shakes hand with every other person. If there was a total of 28 handshakes in the party, then how many persons are present there ?
There are 8 points in a plane out of which 3 are collinear. How many straight lines can be formed by joining them ?
Here n=8, m=3.
How many quadrilaterals can be formed by joining the vertices of an octagon ?
Required no. of quadrilaterals