Research Aptitude Test - 18

Since out of the 120 ways, there is only one way for putting each letter in the correct envelope.

Hence, the number of ways of putting letters all are not in directed envelopes = 120 - 1 = 119 ways.

Here, the first letter can be put in any one of the 5 envelopes in 5 ways. Second letter can be put in any one of the 4 remaining envelopes In 4 ways. Continuing in this way, we get the total number of ways in which 5 letters can be put into 5 envelopes

= 5 x 4 x 3 x 2 x 1 = 120.

The word EQUATION has exactly 8 letters which are all different.

∴ Number of words that can be formed = number of permutations of 8 letters taken all at a time.

= P(8, 8) = 8!

= 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

= 40320

Total number of candidates = 5 + 2 = 9

In the row of 9 positions, the even places are 2^nd , 6^th and 8^th . Now, number of even places = 4.

Number of women to occupy the even places = 4.

∴ Even places can be filled = P(4, 4) ways

Number of men = 5

∴ The remaining 5 places can be tilted by 5 men = P(5, 5) ways

∴ By the fundamental principle of counting.

∴ The required number of seating arrangements = P(4, 4) x P(5, 5) = 4! x 5!

= 24 x 120 = 2880.

4 different books can be arranged among themselves, in a shelf, in P (4,4)

= 4 x 3 x 2 x 1 = 24 ways.

0.2 x 0.3 = 0.06

The probability that the ball drawn is ol green colour = 4/24 = ⅙

Probability that the ball drawn is not of green colour

Two cards can be drawn from a pack of 52 playing cards in⁵² C₂ ways.

The event that two kings appear in a single draw can appear in ⁴ C₂ ways, i.e. 6 ways.

∴ The probability that the two cards drawn from a pack of 52 cards are kings = 6/1326 = 1/221

Uncle of D is A