10
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

Answer:   C) 246

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 = $C14×C46$ = 4 x 15 = 60

In case II the number of ways = $C24×C36$ = 6 x 20 = 120

In case III the number of ways = $C34×C26$ = 4 x 15 = 60

In case IV the number of ways = $C44×C16$ = 1 x 6 = 6

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

Subject: Permutations and Combinations
Exam Prep: GATE , CAT , Bank Exams , AIEEE
Job Role: Bank PO , Bank Clerk
Q:

If each of the vowels in the word 'MEAT' is kept unchanged and each of the consonants is replaced by the previous letter in the English alphabet, how many four-lettered meaningful words can be formed with the new letters, using each letter only once in each word?

 A) 3 B) 4 C) 1 D) 2

Answer & Explanation Answer: A) 3

Explanation:
Report Error

Filed Under: Permutations and Combinations
Exam Prep: Bank Exams

18 1485
Q:

In a bag containing red, green and pink tokens, the ratio of red to green tokens was 5 : 12 while the ratio of pink to red tokens was 7 : 15. What was the ratio of green to pink tokens?

 A) 25 : 28 B) 36 : 7 C) 8 :25 D) 12 : 7

Answer & Explanation Answer: B) 36 : 7

Explanation:
Report Error

Filed Under: Permutations and Combinations
Exam Prep: Bank Exams

7 1176
Q:

The ratio of the members of blue to red balls in abag is constant. When there were 44 red balls, the number of blue balls was 36. If the number of blue balls is 54, how many red balls will be in the bag?

 A) 68 B) 32 C) 64 D) 66

Answer & Explanation Answer: D) 66

Explanation:
Report Error

Filed Under: Permutations and Combinations
Exam Prep: Bank Exams

25 2285
Q:

If each vowel of the word NICELY is changed to the next letter in the English alphabetical series and each consonant is changed to the previous letter in the English alphabetical series and then the alphabets are arranged in alphabetical order, which of the following will be fourth from the left?

 A) M B) J C) B D) O

Answer & Explanation Answer:

Explanation:

Thus after arranging the letters as per English alphabetical series; we get; Thus 4th letter from the left end will be K.

Report Error

16 2341
Q:

How many such pair of letters are there in the word ‘TROUBLED’ which have as many letters between them in the word as they have between them in the English alphabet?

 A) 2 B) 3 C) 4 D) 5

Answer & Explanation Answer: A) 2

Explanation:

Hence there are two pairs

Report Error

13 1977
Q:

If it is possible to make a meaningful word with the first, the seventh, the ninth and the tenth letters of the word RECREATIONAL, using each letter only once, which of the following will be the third letter of the word? If more than one such word can be formed, give ‘X’ as the answer. If no such word can be formed, give ‘Z’ as the answer.

 A) T B) X C) N D) R

Answer & Explanation Answer: D) R

Explanation:

The first, the seventh, the ninth and the tenth letters of the word RECREATIONAL are R, T, O and N respectively. Meaningful word from these letters is only TORN. The third letter of the word is ‘R’.

Report Error

6 1813
Q:

16 persons are participated in a party. In how many differentways can they host the seat in a circular table, if the 2particular persons are to be seated on either side of the host?

 A) 16! × 2 B) 14! × 2 C) 18! × 2 D) 14!

Answer & Explanation Answer: B) 14! × 2

Explanation:

(16 – 2)! × 2 = 14! × 2

Report Error

Filed Under: Permutations and Combinations
Exam Prep: Bank Exams

3 2526
Q:

From a pack of 52 cards, 3 cards are drawn together atrandom, What is the probability of both the cards are king?

 A) 1/5225 B) 1/5525 C) 5525 D) 1/525

Answer & Explanation Answer: B) 1/5525

Explanation:

n(S) = 52C3 = 132600/6 = 22100

n(E) = 4C3 = 24/6 = 4

Report Error

8 1706