Number of ways of selection of 4 letters of the word "PERFECT" is

Question

Number of ways of selection of 4 letters of the word "PERFECT" is (A) 15 (B) 21 (C) 25 (D) 31

Tardigrade Admin · Accepted Answer

7 letters P arrow 1 E arrow 2 R arrow 1 F arrow 1 C arrow 1 T arrow 1 2 text alike +2 text diff. =1 × 5 C 2=10 text All 4 text different = 6 C 4=15 ⇒ 25

Q. Number of ways of selection of 4 letters of the word "PERFECT" is

15

21

25

31

7 letters
$P \to 1$
$E \to 2$
$R \to 1$
$F \to 1$
$C \to 1$
$T \to 1$
$2 alike + 2 diff. = 1 \times^{5} C_{2} = 10$
$All 4 different =^{6} C_{4} = 15 \Rightarrow 25$

Q. Number of ways of selection of 4 letters of the word "PERFECT" is

15

21

25

31

7 letters P→1 E→2 R→1 F→1 C→1 T→1 2 alike +2 diff. =1×5C2​=10 All 4 different =6C4​=15⇒25

7 letters
$P \to 1$
$E \to 2$
$R \to 1$
$F \to 1$
$C \to 1$
$T \to 1$
$2 alike + 2 diff. = 1 \times^{5} C_{2} = 10$
$All 4 different =^{6} C_{4} = 15 \Rightarrow 25$