## Permutation & Combination Solved Questions For IBPS, SBI and Other Bank Exams - Page 3

**Question 1**

In how many ways, can the letters of the word "TELEVISION" be arranged?

a) 907200 b) 1814400 c) 40320 d) none of these

**Answer : **a) 907200

Solution :

The word television contains 10 letters, namely one T, two E, one L, one V, Two I, one S, one O and one N.

Therefore, required number of ways = 10!/1!2!1!1!2!1!1!1!

= 10!/2!2! = 1 x 2 x 3 x .... x 10 / 4 = 907200

**Question 2**

How many 3 letters words (with or without meaning) can be formed out of the letters of the word, "SWITCHBOARD", if repetition of letters is not allowed?

a) 1000 b) 9900 c) 990 d) none of these

**Answer : **c) 990

Solution :

The word Switchboard contains 11 different letters.

Required number of words = number of arrangements of 11 letters taking 3 at a time.

= 11p3 = 11 x 10 x 9 = 110 x 9 = 990.

**Question 3**

In how many ways can the letters of the word "LIGHT" be arranged(using each letter exactly once) ?

a) 60 b) 120 c) 240 d) none of these

**Answer : **b) 120

Solution :

The word light contains 5 different letters.

Required number of words = number of arrangements of 5 letters taken all at a time = 5p5 = 5! = 120

**Question 4**

In how many ways can the letters of the word " SOLUTION" be arranged so that the vowels always come together?

a) 120 b) 240 c) 24 d) none of these

**Answer : **a) 120

Solution :

In the word SOLUTION, we treat the vowels O U I O as one letter.

Thus, we have SLTN(OUIO).

Now, we have 5 different letters.

Then, required number of words = 5! = 120