5
Q:

# A Committee of 5 persons is to be formed from a group of 6 gentlemen and 4 ladies. In how many ways can this be done if the committee is to be included atleast one lady?

 A) 123 B) 113 C) 246 D) 945

Explanation:

A Committee of 5 persons is to be formed from 6 gentlemen and 4 ladies by taking.

(i) 1 lady out of 4 and 4 gentlemen out of 6

(ii) 2 ladies out of 4 and 3 gentlemen out of 6

(iii) 3 ladies out of 4 and 2 gentlemen out of 6

(iv) 4 ladies out of 4 and 1 gentlemen out of 6

In case I the number of ways = $\inline 4C_{1}\times 6C_{4}$ = 4 x 15 = 60

In case II the number of ways = $\inline 4C_{2}\times 6C_{3}$ = 6 x 20 = 120

In case III the number of ways = $\inline 4C_{3}\times 6C_{2}$ = 4 x 15 = 60

In case IV the number of ways = $\inline 4C_{4}\times 6C_{1}$ = 1 x 6 = 6

Hence, the required number of ways = 60 + 120 + 60 + 6 = 246

Q:

If (1 × 2 × 3 × 4 ........ × n) = n!, then 15! - 14! - 13! is equal to ___?

 A) 14 × 13 × 13! B) 15 × 14 × 14! C) 14 × 12 × 12! D) 15 × 13 × 13!

Answer & Explanation Answer: D) 15 × 13 × 13!

Explanation:

15! - 14! - 13!

= (15 × 14 × 13!) - (14 × 13!) - (13!)

= 13! (15 × 14 - 14 - 1)

= 13! (15 × 14 - 15)

= 13! x 15 (14 - 1)

= 15 × 13 × 13!

4 36
Q:

To fill 8 vacancies there are 15 candidates of which 5 are from ST. If 3 of the vacancies are reserved for ST candidates while the rest are open to all, Find the number of ways in which the selection can be done ?

 A) 7920 B) 74841 C) 14874 D) 10213

Explanation:

ST candidates vacancies can be filled by 5C3 ways = 10

Remaining vacancies are 5 that are to be filled by 12

=> 12C5 = (12x11x10x9x8)/(5x4x3x2x1) = 792

Total number of filling the vacancies = 10 x 792 = 7920

9 334
Q:

A,B,C,D,E,F,G and H are sitting around a circular table facing the centre but not necessarily in the same order. G sits third to the right of C. E is second to the right of G and 4th to the right of H. B is fourth to the right of C. D is not an immediate neighbour of E. A and C are immediate neighbours.

Which of the following is/are correct ?

 A) F is third to the left of B B) F is second to the right of B C) B is an immediate neighbour of D D) All of the above

Answer & Explanation Answer: B) F is second to the right of B

Explanation:

From the given information, the circular arrangement is

Here F is second to the right of B and the remaning all are wrong.

5 198
Q:

Nine different letters of alphabet are given, words with 5 letters are formed from these given letters. Then, how many such words can be formed which have at least one letter repeated ?

 A) 43929 B) 59049 C) 15120 D) 0

Explanation:

Number of words with 5 letters from given 9 alphabets formed = $\inline \fn_jvn 9^{5}$

Number of words with 5 letters from given 9 alphabets formed such that no letter is repeated is = $\fn_jvn 9_{}^{P}\textrm{5}$

Number of words can be formed which have at least one letter repeated = $\inline \fn_jvn 9^{5}$ - $\fn_jvn 9_{}^{P}\textrm{5}$

= 59049 - 15120

= 43929

8 327
Q:

In how many different ways can the letters of the word 'ABYSMAL' be arranged ?

 A) 5040 B) 3650 C) 4150 D) 2520

Explanation:

Total number of letters in the word ABYSMAL are 7

Number of ways these 7 letters can be arranged are 7! ways

But the letter is repeated and this can be arranged in 2! ways

=> Total number of ways arranging ABYSMAL = 7!/2! = 5040/2 = 2520 ways.