A girl named TUSHITA is doing an experiment in which she has to arrange
the letters of her name in all possible orders and note the observations. Help
her to find the answers of the following:-
(a) Number of words starting with A
(i) 360 (ii) 720 (iii) 1440 (iv) 2880
(b) Number of words having T at extremes
(i) 72 (ii) 120 (iii) 240 (iv) 480
(c) Words having only consonants
(i) 48 (ii) 24 (iii) 12 (iv) 6
(d) Words in which vowels occupy even places
(i) 108 (ii) 72 (iii) 24 (iv) 120
Answers
Answer:
a.720
b.120
c.24
d.120
Step-by-step explanation:
Answer:
a) 360
b) 120
c) 12
d) 72
Step-by-step explanation:
a) For number of words starting with "A", fix that spot and now we are left with 6 letterS TUSHIT.
Number of ways to arrange 6 letters is 6! = 720. But as T is occurring twice we divide the ans by 2! . So totals ways are 6!/2! = 720/2 = 360.
b) Number of words with T at extremes, i.e.
T _ _ _ _ _ T . So letters that are remaining needs to get arranged, i.e. USHIA. Number of ways to arrange 5 letters is 5! = 120.
c) The consonants present are "TSHT" and number of ways to arrange is 4!/2! = 12.
d) Let the 7 places be denoted by P1, P2, .... , P7.
The vowels present are "UIA" and they need to arrange in places P2, P4 and P6 i.e. total ways are ³P = 6, and arranging remaining 4 letters "TSHT" in remaining 4 places is 4!/2! = 12.
So total ways are 6*12 = 72.
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