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Aptitude Permutations Practice Q&A-Easy

2880.A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?
32
48
64
96
Explanation:

We may have[1 black and 2 non-black] or [2 black and 1 non-black] or [3 black].

Required number of ways = (3C1 x 6C2) + (3C2 x 6C1) + (3C3)
=[($ 3 \times 5 $ \dfrac{6 \times 5}{2 \times 1} $)]$ + $ [(\dfrac{3 \times 2}{2 \times 1} \times 6]$ + 1
= (45 + 18 + 1)
= 64.
2881.How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?
5
10
15
20
Explanation:

Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.

The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.

The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.

$\therefore$ Required number of numbers = $\left(1 \times 5 \times 4\right)$ = 20.

2883.In how many ways can the letters of the word LEADER be arranged?
72
144
360
720
Explanation:

The word LEADER contains 6 letters, namely 1L, 2E, 1A, 1D and 1R.

$\therefore$ Required number of ways =$ \dfrac{6!}{(1!)(2!)(1!)(1!)(1!)} $= 360.
2884.How many 6 digit telephone numbers can be formed if each number starts with 35 and no digit appears more than once?
720
360
1420
1680
Explanation:

The first two places can only be filled by 3 and 5 respectively and there is only 1 way for doing this.

Given that no digit appears more than once. Hence we have 8 digits remaining (0,1,2,4,6,7,8,9)

So, the next 4 places can be filled with the remaining 8 digits in 8P4 ways.

Total number of ways = 8P4=8×7×6×5=1680

2886.An event manager has ten patterns of chairs and eight patterns of tables. In how many ways can he make a pair of table and chair?
100
80
110
64
Explanation:

He has 10 patterns of chairs and 8 patterns of tables

A chair can be selected in 10 ways.

A table can be selected in 8 ways.

Hence one chair and one table can be selected in 10×80 ways =80ways

2890.How many 4-letter words with or without meaning, can be formed out of the letters of the word, LOGARITHMS, if repetition of letters is not allowed?
40
400
5040
2520
Explanation:

LOGARITHMS contains 10 different letters.

Required number of words= Number of arrangements of 10 letters, taking 4 at a time.

= 10P4=$\left (10 \times 9 \times 8 \times 7\right)$= 5040.

2891.A box contains 4 red, 3 white and 2 blue balls. Three balls are drawn at random. Find out the number of ways of selecting the balls of different colours?
62
48
12
24
Explanation:

1 red ball can be selected in 4C1 ways.

1 white ball can be selected in 3C1 ways.

1 blue ball can be selected in 2C1 ways.

Total number of ways

= 4C1 × 3C1 × 2C1

=4×3×2=24

2892.25 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?
None of these
600
576
625
Explanation:

He can go in any of the 25 buses [25 ways].

Since he cannot come back in the same bus, he can return in 24 ways.

Total number of ways =25×24=600

2894.In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?
266
5040
11760
86400
Explanation:
Required number of ways = (8C5 x 10C6)
= (8C3 x 10C4)
= $ \left(\dfrac{8 \times 7 \times 6}{3 \times 2 \times 1} \times\dfrac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1} \right) $
= 11760.
2897.Find out the number of ways in which 6 rings of different types can be worn in 3 fingers?
120
720
125
729
Explanation:

The first ring can be worn in any of the 3 fingers [3 ways].

Similarly each of the remaining 5 rings also can be worn in 3 ways.

Hence total number of ways

=3×3×3×3×3×3 =$3^6$ =729

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