Question

The number of ways that the letters of the word
“PERSON” can be placed in the squares of the
adjoining figure so that no row remains empty
R-1
R-
R-​

Answer 1

Step-by-step explanation:

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Asked on December 20, 2019 by

Parveen Dhir

The number of ways in which the letters of the word PERSON can be placed in the squares of the given figure so that no row remains empty is

127577

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ANSWER

There are 6 different letters. We have to select 6 squares, taking at least one from each row and then arranging in each selection. Let us first select places in each row such that no row remains empty.

R

1

R

2

R

3

Number of selections

1 1 4

2

C

1

×

2

C

1

×

4

C

4

=4

1 2 3

2

C

1

×

2

C

2

×

4

C

2

=8

2 1 3

2

C

2

×

2

C

1

×

4

C

3

=8

2 2 2

2

C

2

×

2

C

2

×

4

C

2

=6

Therefore, the total number of selections of 6 squares is 4+8+8+6=26. For each selection of 6 squares, the number of arrangements of 6 letters is 6!=720. Hence, the required number of ways is 26×720=18720.