Q1.
nc10 = nc12 , then the value of n .
Solution.
ncx = ncy
if x = y or x + y = n
n = 10 + 12 = 22
Solution
Q2.
In how many ways can 6 students be arranged in a row .
Solution
6p6 = 6!
Solution
Q3.
In how many ways 5 rings of different types can be wore in a fingure .
Solution.
45
Solution
Q4.
Find the value of (n + 2)! - (n + 1)!
Solution.
(n+2) (n+1)! - (n+1)!
(n + 1)! {(n + 2) - 1} = (n + 1)! (n + 1)
(n + 1) (n + 1)!
Solution
Q5.
A number lock consists of three rings each marked with 10 digits (0,1,2,------,9) . How many unsuccessful attempts to open the lock .
Solution.
10 x 10 x 10 = 1000 (total attempt) out of 1000 attempt one attempt will open the lock . So, total unsuccesful attempts are 1000 - 1 = 999 .
Solution
Q6.
Find number of ways in which 7 men can be arranged in a row so that three particular men are seating together .
Solution.
Three persons are seating together so these three persons will be consider as a single person = 5! . 3!
Note :
All three persons can interchange their position .
Solution
Q7.
How many numbers of 3 digits can be formed from the digits 0,1,2,3,4, if the digits can be repeated in the same number .
Solution.
hundred,s place can be filled by 4 ways rest of the place can be filled by 5 ways = 4 x 5 x 5 = 100 ways .
Solution
Q8.
Find the number of permulations of 8 distinct objects taken 3 at a time when a particular object is never included in the permulations.
Solution.
As n-1pr one object is not included
7p3 = 210 .
Solution
Q9.
In how many ways can a examination papers be permutated so that the least and the best papers are never together (marks secured).
Solution.
= Total arrangements - arrangements in whih both papers are simultaneous
= 9p9 -
8p8 . 2! = 9! - 2.8! = 9.8! - 2.8!
= 8!(9 - 2) = 7.8 !
Note : The papers which are simultaneous consider as single paper .
Solution
Q10.
Three dice are rolled . Find the number of possible outcomes in which at least one die shows 4 .
Solution.
= Total number of possible outcomes - number of possible outcomes in which 4 does not appear on any dice .
= 63 - 53 = 216 - 125 = 91
Solution
