Permutations and Combinations
The probability that, on the examination day, the student 𝑆1 gets the previously allotted seat 𝑅1, and NONE of the remaining students gets the seat previously allotted to him/her is
For 𝑖 = 1, 2, 3, 4, let 𝑇𝑖 denote the event that the students 𝑆𝑖 and 𝑆𝑖+1 do NOT sit adjacent to each other on the day of the examination. Then, the probability of the event 𝑇1 𝑇2 𝑇3 𝑇4 is
(i) Let α1 be the total number of ways in which the committee can be formed such that the committee has 5 members, having exactly 3 boys and 2 girls.
(ii) Let α2 be the total number of ways in which the committee can be formed such that the committee has at least 2 members, and having an equal number of boys and girls.
(iii) Let α3 be the total number of ways in which the committee can be formed such that the committee has 5 members, at least 2 of them being girls.
(iv) Let α4 be the total number of ways in which the committee can be formed such that the committee has 4 members, having at least 2 girls and such that both M1 and G1 are NOT in the committee together.
|P.||The value of α1 is||1.||136|
|Q.||The value of α2 is||2.||189|
|R||The value of α3 is||3.||192|
|S.||The value of α4 is||4.||200|
The correct option is:
Let Tn be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If Tn + 1 − Tn = 10, then the value of n is:
The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is
The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, is
Consider all possible permutations of the letters of the word ENDEANOEL.
Match the Statements/ Expressions in Column I with the statements/ Expressions in Column II and indicate your answer by darkening the appropriate bubbles in the matrix given in the ORS.
|(A)||The number of permutations containing the word ENDEA is||(p)||5!|
|(B)||The number of permutations in which the letter E occurs in the first and the last positions is||(q)|
|(C)||The number of permutations in which none of the letters D, L, N occurs in the last five positions is||(r)|
|(D)||The number of permutations in which the letters A, E, O occur only in odd positions is||(s)|
If r, s and t are prime numbers and p and q are positive integers such that the LCM of p and q is r2t4s2, then the number of ordered pair (p, q) is