Permutation and Combination PDF and Quiz For SBI Clerk Pre, IBPS Clerk Pre, IBPS RRB

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Directions: Study the following set of questions carefully and answer the questions given below.
1
16 persons shake hands with one another in a party. How many shake hands took place?
» Explain it
B
Total possible ways = 16C2

=   16 × 15  = 120
2 × 1

Hence, option B is correct.

2
How many 3 - letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
» Explain it
A
The word 'LOGARITHMS'' has 10 different alphabets

Hence, the number of 3-letter words (with or without meaning) formed by using these letters = (10P3)

= 10 × 9 × 8 = 720

Therefore, option (A) is correct.
3
In how many different ways can the letters of word ‘POPULAR’ be arranged?
» Explain it
E
The total no. of letters in the word POPULAR is 7 where P appears twice

Reqd no. of ways =  7!  
2!

=   7 × 6 × 5 × 4 × 3  =  2520.

Hence, option E is correct.
 
4
A team of 7 children is to be selected out of 7 girls and 5 boys such that it contains at least 5 girls. In how many different ways can the selection be made?
» Explain it
B
A team of seven children consisting of at least five girls can be formed in the following ways

Case I: When five girls and two boys are selected 7C5 × 5C2

Case II: When six girls and one boys are selected 7C6 × 5C1

Case III: When seven girls and no boy are selected 7C7

Reqd no. of selections =  7C5 × 5C2 + 7C6 × 5C1 + 7C7

=   7 × 6  ×  5 × 4  + 7 ×   + 1 
2 1

= 21 × 10 + 7 × 5 + 1 = 210 + 35 + 1 = 246

Hence, option B is correct.

 
5
In how  many different ways can the letters of word RABBIT be arranged?
» Explain it
A
Required no. of ways =  6!  = 360 ways
2!


Hence, option A is correct.