permutations and combination mcq Model Questions & Answers, Practice Test for ibps rrb so officer sclae 2 3 single exam 2024

Answer: (c)

Putting l Englishman in a fixed position, the remaining 6 can be arranged in 6! 720 ways, For each such arrangement, there are 7 positions for the 7 Americans and they can be arranged in 7! ways.

Total number of arrangements = 7! × 6! = 3628800

Answer: (b)

n(S) = $^12c_3 = {12 × 11 × 10}/{3 × 2} = 2 × 11 × 10$ = 220

No. of selection of 3 oranges out of the total 12 oranges

= $^12c_3 = 2 × 11 × 10$ = 220.

No. of selection of 3 bad oranges out of the total 4 bad oranges = $^4c_3$ = 4

∴ n(E) = no. of desired selection of oranges

= 220 – 4 = 216

∴ P(E) = ${n(E)}/{n(S)}= 216/220 = 54/55$

Answer: (b)

From each railway station, there are 19 different tickets to be issued.

There are 20 railway station So, total number of tickets = 20 × 19 = 380.

Answer: (a)

Possible arrangements are :

${7!}/{2! 2!}$ = 1260

[division by 2 times 2! is because of the repetition of E and R]

Answer: (a)

(a) The word STABLE has six distinct letters.

∴ Number of arrangements = 6 !

= 6 × 5 × 4 × 3 × 2 × 1 = 720

(b) The word STILL has five letters in which letter 'L' comes twice.

∴ Number of arrangements

= ${5!}/2 = 60$

(c) The word WATER has five distinct letters.

∴ Number of arrangements = 5 ! = 5 × 4 × 3 × 2× 1 = 120

(d) The word 'NOD' has 3 distinct letters.

∴ Number of arrangements = 3 ! = 6

(e) Number of arrangements = 4 ! = 24