Capgemini Permutation and Combination Quiz-1

Since to form a 5-digit number 0 cannot be placed at ten-thousandth position.

Therefore, the number of possible arrangements can be 4*5*5*5*5 = 2500

Number of ways = ¹⁰C₄ x ⁵C₂ = 21 x 100 = 2100

Total attempts possible with three rings = 5*5*5*5*5 = 3125

Out of 3125 attempts only 1 will be a successful attempt.
Therefore, total number of failed attempts  = 3125-1= 3124

Each of the 10 mangoes can be placed in any of the 5 boxes, that is each mangoes has possible 5 arrangements.

First mango can be arranged in 5 ways.

Second can be arranged in 5 ways.

There are total 8 alphabets in the “STRAIGHT” out of which only 2 are Vowels (A and I)

Number of consonants = 6

Let the position of letter be:

• (2) (3) (4) (5) (6) (7) (8)

Let n be the number of teams.
ⁿC₂ = 21
(n(n-1)/2) = 21
⇒ n(n-1) = 42 ∴
⇒ n = 7

The number of four–digit telephone numbers which can be formed using the digits of 0, 1, 2,...., 9 is 10⁴.
The number of four digit telephone numbers which have none of their digits repeated is ¹⁰P₄ = 10 ×9 ×8 ×7 = 5040
Hence the required number =10⁴- 5040 = 4960

JUMBLE is a six-lettered word. Since the rearranged word has to start with a vowel, the first letter can be either U or E. The balance 5 letters can be arranged in ⁵P₅ or 5! ways. Total number of words = 2 × 5! = 240.

The candidate will fail if he fails either in 1 or 2 or 3 or 4 or 5 subjects, ∴ Required number of ways ⁵C₁ + ⁵C₂ + ⁵C₃ + ⁵C₄ + ⁵C₅ = 31