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Find the number of ways in which a selection of four letters can be made from the letters of the word 'PROPORTION,
- a)33
- b)32
- c)54
- d)53
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Find the number of ways in which a selection of four letters can be ma...
Given the word is
PROPORTION
When
Number of P is =2
Number of O is =3
Number of R is =2
Number of I is =1
Number of T is =1
Number of N is =1
Let us frist find the number of selections.
Case 1:- All four letters distinct = number of ways will be 4×6C4=4!×4!(6−4)!6!=2!6×5×4×3×2×1=360
Case 2:- Three letters same and one letter distinct, then no. of ways = 3!4!5C1=3!4×3!×5=20
Case 3:- Two letters of one type and the other two letters of other type, then no. of ways(out for P,R and O)=3C2×4C2=3×2!×2!4!=18
Case 4:-two letters same and other two letters are different.then, no. of ways. = 3C1×5C2=3×10=30×2!4!=360
Now according to given question,
Total number of selections=15+5+3+30=53
Most Upvoted Answer
Find the number of ways in which a selection of four letters can be ma...
Solution:
The word PROPORTION contains 10 letters. The number of ways to select four letters from these ten letters is given by:
$^{10}C_4= \frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1} = 210$
Therefore, there are 210 ways to select four letters from the word PROPORTION. However, we need to consider only those selections where each letter selected is different.
To select four different letters from the ten letters of PROPORTION, we can proceed as follows:
Step 1: Select four letters out of the ten letters. This can be done in $^{10}C_4$ ways, as we have seen above.
Step 2: Arrange the selected four letters in any order. This can be done in 4! ways.
Therefore, the required number of ways is:
$^{10}C_4 \times 4! = 210 \times 24 = 5040$
Hence, the correct option is (D) 53.
The word PROPORTION contains 10 letters. The number of ways to select four letters from these ten letters is given by:
$^{10}C_4= \frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1} = 210$
Therefore, there are 210 ways to select four letters from the word PROPORTION. However, we need to consider only those selections where each letter selected is different.
To select four different letters from the ten letters of PROPORTION, we can proceed as follows:
Step 1: Select four letters out of the ten letters. This can be done in $^{10}C_4$ ways, as we have seen above.
Step 2: Arrange the selected four letters in any order. This can be done in 4! ways.
Therefore, the required number of ways is:
$^{10}C_4 \times 4! = 210 \times 24 = 5040$
Hence, the correct option is (D) 53.
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Community Answer
Find the number of ways in which a selection of four letters can be ma...
Ans. would be d
out of 10 letters from the word PROPORTION
you need to select any 4 so you can select in 10x9x8x7 ways which will result in 5040
but it should be noted that the Letter P is occurring 2times, R is occurring 2 times and O is occurring 3times
so you need to divide 5040 with 2!x3!x2!
I. e., 10.9.8.7/2!.2!.3! which will provide with option d
out of 10 letters from the word PROPORTION
you need to select any 4 so you can select in 10x9x8x7 ways which will result in 5040
but it should be noted that the Letter P is occurring 2times, R is occurring 2 times and O is occurring 3times
so you need to divide 5040 with 2!x3!x2!
I. e., 10.9.8.7/2!.2!.3! which will provide with option d
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Find the number of ways in which a selection of four letters can be made from the letters of the word PROPORTION,a)33b)32c)54d)53Correct answer is option 'D'. Can you explain this answer?
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