## Probability Questions for IBPS Clerk

### Probability Questions for IBPS Clerk 2015 Exam

**1.** In how many ways letter of the world BANKING can be arranged so that vowels always come together? **(IBPS Clerk 2015)**

(a) 240

(b) 120

(c) 720

(d) 540

(e) None of these

**Probability Questions for IBPS Clerk 2015 Answers**

**1.** (c)

[(6!)/(2!)] × (2!)= 360 × 2 = 720 [(6!)/(2!)] = letters formed, 2!-Vowels

### Probability Questions for IBPS Clerk 2012 Exam

**1.** Which of the following words can be written in 120 different ways? **(IBPS Bank Clerk 2012)**

(a) STABLE

(b) STILL

(c) WATER

(d) NOD

(e) DARE

**Probability Questions for IBPS Clerk 2012 Answers**

**1.** (c)

(1) The word STABLE has six distinct letters.

∴ Number of arrangements = 6 !

= 6 × 5 × 4 × 3 × 2 × 1 = 720

(2) The word STILL has five letters in which letter ‘L’ comes twice.

∴ Number of arrangements

\(= \frac { 5 ! } { 2 } = 60\)

### Probability Questions for IBPS Clerk 2011 Exam

**1.** In how many different ways can the letters of the word ‘BELIEVE’ be arranged? **(IBPS Clerk 2011)**

(a) 840

(b) 1680

(c) 2520

(d) 5040

(e) None of these

**2.** In how many different ways can the letters of the word ‘VIRTUAL’ be arranged among themselves? **(IBPS Clerk** **2011)**

(a) 840

(b) 5040

(c) 2520

(d) 1680

(e) None of these

**3.** In how many different ways can the letters of the word ‘MARKERS’ be arranged? **(IBPS Clerk 2011)**

(a) 840

(b) 5040

(c) 2520

(d) 1680

(e) None of these

**4.** In how many different ways can the letters of the word’ ‘VENTURE’ be arranged? **(IBPS Clerk 2011)**

(a) 840

(b) 5040

(c) 1260

(d) 2520

(e) None of these

**5.** In how many different ways can the letters of the word ‘TROUBLE’be arranged? ’ **(IBPS Clerk 2011)**

(a) 840

(b) 5040

(c) 1260

(d) 2520

(e) None of these

**Probability Questions for IBPS Clerk 2011 Answers**

**1.** (a)

The word BELIEVE consists of 7 letters in which E comes thrice.

∴ Required number of arrangements \(= \frac { 7 ! } { 3 ! }\)

\(= \frac { 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 } { 3 \times 2 \times 1 } = 840\)

**2.** (b)

There are seven letters in the word “VIRTUAL”.

Therefore, number of different ways in which these letters can be arranged

= 7! = 7 × 6 × 5 × 4 × 3 × 2 = 5040

**3.** (c)

The word “MARKERS” has seven letters, and seven letters can be arranged ! 7 ways.

But the letter ‘R’ appears twice.

∴ The number of possible ways

\(\frac { 7 ! } { 2 ! } = 2520\)

**4.** (d)

There are 7 letters in the given word VENTURE in which E comes twice.

∴ Total number of ways

\(= \frac { 7 ! } { 2 ! } = 7 \times 6 \times 5 \times 4 \times 3 = 2520\)

**5.** (b)

Required ways = 7! = 7 × 6 × 5× 3 × 2 × 1 = 5040

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