Qm- Session #04-permutations And Combinations
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Session No. 4 Chapter No. # 02
Basics of Mathematics Key concepts : Permutations and Combinations,
Permutations • Each of the arrangements that can be made by taking some or all of a number of things/objects is called a Permutation. • nPr denotes the permutation of n dissimilar objects taken r at a time.
Permutation of 4 alphabets A,B,C and D taken 2 at a time. AB
AC
AD
BA
BC
BD
CA
CB
CD
DA
DB
DC
n ! n Pr = (n − r )!
Where n ! = n x (n-1) x (n-2) x …..x 1 e.g. 5 ! = 5 x 4 x 3 x 2 x 1 = 120 4
P2 =
4! (4-2) !
= 4 x 3 x 2 x 1 = 12 2x1
Combination • Each of the selections that can be made by taking some or all of a number of things/objects is called a Combination. • nCr denotes the Combination of n dissimilar objects taken r at a time.
Combination of 4 alphabets A,B,C and D taken 2 at a time. AB
AC
AD
BC
BD
CD
n ! n Cr = r!(n − r )!
If P3 =210 find the value of n. n
If
7
Pr =210Find r.
RTO Department at Pune wants to allot three digit number plates to registered vehicles. The digits can be chosen from 1,2, 3 and 4. For how many vehicles the numbers can be alloted?
At Annual General Meeting of Reliance Infocomm every person shakes with every other person in the meeting hall. Find the number of handshakes if there were 21 persons present in the meeting.
Find the number of words that can be formed with the help of the letters of the word DELHI, which begins with D.
In how many ways 5 chocolates can be taken from a box containing 10 chocolates?
Mr. John has to visit Ajanta Caves, there are 5 different routes from Aurangabad to Ajanta. How many total number of ways are available for John if he does not want to return by the same way?
At a birthday party there were 7 white and 9 orange balloons. Abhijit wanted one balloon of each color. In how many ways he can select the balloons.
There are 5 shops in the shoe market. Four friends Bhushan, Sunil, Mahavir and Parimal want to purchase shoes from different shops. In how many ways they can do it?
Basics of Mathematics Key concepts : Permutations and Combinations,
Permutations • Each of the arrangements that can be made by taking some or all of a number of things/objects is called a Permutation. • nPr denotes the permutation of n dissimilar objects taken r at a time.
Permutation of 4 alphabets A,B,C and D taken 2 at a time. AB
AC
AD
BA
BC
BD
CA
CB
CD
DA
DB
DC
n ! n Pr = (n − r )!
Where n ! = n x (n-1) x (n-2) x …..x 1 e.g. 5 ! = 5 x 4 x 3 x 2 x 1 = 120 4
P2 =
4! (4-2) !
= 4 x 3 x 2 x 1 = 12 2x1
Combination • Each of the selections that can be made by taking some or all of a number of things/objects is called a Combination. • nCr denotes the Combination of n dissimilar objects taken r at a time.
Combination of 4 alphabets A,B,C and D taken 2 at a time. AB
AC
AD
BC
BD
CD
n ! n Cr = r!(n − r )!
If P3 =210 find the value of n. n
If
7
Pr =210Find r.
RTO Department at Pune wants to allot three digit number plates to registered vehicles. The digits can be chosen from 1,2, 3 and 4. For how many vehicles the numbers can be alloted?
At Annual General Meeting of Reliance Infocomm every person shakes with every other person in the meeting hall. Find the number of handshakes if there were 21 persons present in the meeting.
Find the number of words that can be formed with the help of the letters of the word DELHI, which begins with D.
In how many ways 5 chocolates can be taken from a box containing 10 chocolates?
Mr. John has to visit Ajanta Caves, there are 5 different routes from Aurangabad to Ajanta. How many total number of ways are available for John if he does not want to return by the same way?
At a birthday party there were 7 white and 9 orange balloons. Abhijit wanted one balloon of each color. In how many ways he can select the balloons.
There are 5 shops in the shoe market. Four friends Bhushan, Sunil, Mahavir and Parimal want to purchase shoes from different shops. In how many ways they can do it?
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